It's possible Vegeta's confidence was shaken or he was lacking in interoception after his senzu - due to being so focused on Goku's power up and the possibility of someone else beating him to SSJ - so he didn't notice his ki upgrade initially.
But by the time he meets 530K 1st form Freeza, thought he's nervous, he's still confident enough to fight him (rather than trying to use a distraction to escape). And then rather than trying to inflict maximum damage on Freeza while they're evenly matched, he tells him to transform - not the actions he'd take if unconfident about being near 500K (Btw, did he have a death wish? Was he hoping fighting Freeza's 2nd form could allow him to unlock SSJ?). He obviously believed he was close to 530K (I'd say at mimumum however much weaker Piccolo was than Nappa, but before meeting Freeza. I'm going through the pages to see if there's any clue when he believed it or when he powered up.
In the below page (ch283), he seems to realise he's stronger than Jeice - he says
"tch, so you knew" when Goku says
"you've recovered from near death, your power should've gone up. [Jeice] is no longer an opponent you can't handle". If he knew he's significantly stronger than what Goku showed vs Burta/Jeice, he probably would've been offended by being compared to Jeice and said that he's stronger. His ego is too big for him to focus on getting the dragon balls, rather than one-upping Goku first.
He also says later (second image below) that Goku and Ginyu have equal PLs and will take each other out to leave Vegeta to do as he pleases (ie use the dragon balls) - if he's already decently above Goku and Ginyu (90-100K is enough), he'd already be free to do as he pleases, without them weakening each other first. It all points to Vegeta believing he's only moderately stronger than Jeice.
(Note: it's also possible Vegeta's "tch, so you knew" was only referring to Goku's knowledge of zenkais and
not to Vegeta's ability to handle Jeice - I don't remember if either Vegeta/Goku had discussed the existence of zenkais before this chapter or if Krillin/Gohan had told Vegeta they knew about zenkais - and that when Vegeta ran away he wasn't 100% sure if he could handle Jeice and he only became sure of it after spending some time alone.)
Anyway, he even says "once I'm granted eternal life I'll finally have a
chance of besting Freeza" - indicating he doesn't believe he's near Freeza's 530K PL, as to even have a
chance he needs to be immortal first. If he was 500K or so, he'd have a chance even without immortality - we see he believes this later, when he challenges Freeza to turn to his 2nd form, with zero doubt in his ability to win until he actually feels the 2nd form's ki.
Next, Vegeta stops Jeice (ch289, pg7), so he can get the password from Krillin/Gohan and possibly to help him fight Freeza if he doesn't get immortality in time (since he's seen the invocation not work).
I was also thinking he could've fought Jeice because he thinks bloodlust will help him be a SSJ (I find the psychological stuff interesting), until I realised what the "invocation" means lol.
Anyway, below he says he's "
just now realised" something about his power. This is the earliest I think he knows he's become very strong. (Or it could be the (false) belief he could be a SSJ.) We can say with 100% certainty that Vegeta here senses he's much stronger than Jeice, because he the way he's talking is how he talks to opponents when he's confident he's able to crush them (eg Cui, Dodoria, 1st form Zarbon). And his self-confidence makes me think he can't be underestimating of his power at this point, even if he may have been earlier. He's feeling his power as much as he can, he's revelling in it to convince himself he's the most powerful saiyan who ever lived, ever will live and ever could live.
Is he saying his PL's continuously rising? He's not saying that. It could just be previous growth.
He also says he's gone beyond the normal saiyan limits. Does this definitively mean he believes he's currently surpassed Goku? No - he could still believe he's weaker than Goku or only as strong as him. It just refers to him surpassing the typical ≈15-20K "normal" limit of saiyan power. But he surpassed that a while ago, so why would he only start thinking about it now? It's simply more of his narcissistic delusion (which often helps him to achieve things, until he goes too far lol), awaked by a fear of another saiiyan becoming a SSJ, so he's started to delude himself into believing all his power increases on Namek (starting with Zarbon) were due to him being a SSJ-in-waiting. He rationally should think "Goku and Gohan have also gone past those limits", but he's just going crazy - he says (paraphrasing) it's "not just because I'm gifted" - he knows the three saiyans on Namek are all gifted, but he believes his increase is due to some other special quality, even though he has zero evidence of it.
But yeh as I said, I think he's realised whatever power he has here.
Then he easily kills Jeice without difficulty, though he does put some effort into this attacks. After killing Jeice he believes/knows at minimum he's roughly as strong as Goku and Ginyu were when he left them behind.
After Ginyu is defeated, Vegeta doesn't kill the earthlings. He gives the reason that he needs help to summon the dragon (they're on good terms with the Namekians) and that Goku could help in the fight with Freeza and in his mind thinks he'll kill them after defeating Freeza. What's this say about his belief in his power? He doesn't know Dende will arrive before Goku's zenkai, so has to be confident he's at minimum as strong as what Goku will be post-zenkai. This is because he needs to be able to either kill Goku before fighting Freeza (while beating up a Namekian to get the password/translation to wish for immortality - for this he needs to be much stronger than Goku) or after fighting Freeza (kill Freeza in a hard battle, then immediately kill Goku - he only needs to be as strong as Goku, since he'll take advantage of Goku's guard being down).
When he finds out about Porunga being summoned, he tells them they need to make him immortal to beat Freeza - I don't think this was his original plan, I believe he just planned to beat the password out of whoever he needed to, but now he's in a rush as he senses Freeza arriving, so instead of taking time to beat it out of them, he's trying to convince them. He'd never seen what a dragon summoning looks like before this, so he had no idea it would be big enough to attract Freeza from anywhere on the planet - if he had known that, then yeh his plan would have probably been to convince them instead, so he doesn't have to spend too long with Porunga summoned/the sky being black.
summary: I dunno tbh.
BUT my opinion after reading it is I do think Vegeta just didn't know the depths of his own power. 1. He was freaked out by Goku. 2. Then he talked about Goku/Ginyu needing to be out of the way. 3. Then he got all super confident later, after spending a little time on his own - he realised the power here. 4. Then he tells Freeza that Gohan is still getting stronger - why wouldn't he also say "I'm getting stronger"? Because he was never getting stronger continuously - he just suddenly realised his power before talking to Jeice.
