And Goku doesn't know when or how Hit is going to attack him. That's basically the whole reason Vegeta lost. Goku isn't totally off guard, which is why he's not being one shot again, but he still can't do anything.
Comparing Goku's situation with Vegeta doesn't make sense like at all. Vegeta didn't know at all anything about TS while Goku got informed by other people, showed to be able to counter it while also giving himself an idea fighting Vegeta and predicted it accurately.
When someone is stronger in stats than Hit, they can basically overpower all of his haxed abilities as nobody whose power has surpassed him has been shown to be affected by his hax. When Goku or Jiren surpassed his TS, there's nothing it can do to them.
Goku by himself said that Hit can no longer keep up with him even with TS once he used Kaioken. So, yes TS only affects people with lesser power.
Kunshi jumped on the edge of the arena, Hit beating him there isn't impressive at all. Kunshi and Dyspo both took hits from characters well beyond their level: Hit, SSJG/B Goku, even Golden Freeza later for Dyspo.
I can concede in the fact that Kunshi is weird to be a case, but we can justify it by Goku never acceding to the full exent of SSj Blue power on those episodes before Jiren. Dyspo only received one kick from SSjG Goku and was able to at least get up on his feet against Golden Freeza, regardless of everything, it's not like they're SSJ-SSJ3 levels of power to get oneshotted or lack the durability to receive these attacks. Dyspo in his base form is like a SSjG in terms of strength but his speed make him lethal.
Hit was totally done after receiving the glare. After that, Hit just did that one blast to finish him. Goku took the glare more than once and kept fighting.
He wasn't knocked even after receiving a direct blast fron Jiren it just managed to throw him out of the arena. Him receiving a combo like that is far more impressive than the likes of Golden Freeza or SSjB Vegeta who got oneshotted by one hit (Freeza) or one blast (Vegeta).
In fact, Hit couldn't do anything to Jiren the whole fight. He relies on timeskip and similiar powers the whole fight and gets stomped whenever Jiren gets his hands on him.
The fact that he has the speed reaction to block whenever he hits him and Jiren shows to be able to create impacts while punching him shows that all of his stats got better once he is adapting.
No, it's that timeskip has the same effect as being faster since you can't see or react to his attacks unless you predict them. Goku can't expect anything if Hit already attacks before he can even think.
And that can only be done with an superior speed as shown with Dyspo, or a superior power like Kaioken Goku or Jiren. As well as knowing in what consists his TS ability.
Goku only notices that Kamehameha won't last long after that gif. After the Kamehameha Goku punches him once before giving up and Hit can barely stand up.
That was after both of them reached their limits and Hit manage to dodge him. Goku consistently is shown to want to finish off Hit with whatever method it takes, the fact that this Hit can react to Kaioken x10 Goku's speed while he couldn't do it initially with regular Kaioken Goku's is also an example at how he got better reflexes which can only be done with an improvement in power (at this point he ain't relying on TS).
The scans you posted have several characters, including Hit himself, say he can't raise his power.
One thing is being unable to raise his power through power up in the usual way (screaming/transforming) and other being unable to power-up in any way or shape, which Hit encountered a way to counter that limitation and be able to improve his general stats. Maybe initially it was only focused in his TS, but then we got and shown how many improvements he can get by either speed, strength or durability.