Нужно jusT, а не jusR

Перфект подразумевает УЖЕ, т.е. процесс уже начался и в настоящий момент продолжается.
Если употребить простое прошедшее (Past Simple), то было бы понятно, что процесс в прошлом начался, или начинался, но продолжается ли он сейчас, было бы неясно.
В разговорной речи с JUST употребляют и Past Simple:
A: Would you like to have some snack?
B: No, thanks, I just ate.
A: Не хочешь что-нибудь перекусить?
В: Нет, спасибо, я только что поел.
Однако, по формально грамматике надо сказать ”I’ve just eaten” ( = я только что поел, и СЕЙЧАС сыт).

уже - already
just - только что, недавно

In this case, the perfect doesn't indicate "already," it signals a change in someone's situation that has a significant bearing on their life. I call it the "newsworthy" use of the perfect because you mostly use it to "announce" that something happened, rather than just relay it as fact.

To illustrate this... "Andrew just started night school" is just a fact. However "Andrew has just started night school" has some bearing because, perhaps, Andrew was a drug addict and has rehabilitated himself - and this is a big step for him because he had never finished high school because of addiction.

In another example: "I quit smoking" is just a fact: [workmates] A: Are you chewing gum? I've never seen you chew gum before - you don't seem like the gum type))) B: Well, I quit smoking and apparently chewing gum helps with the cravings. Here "I quit smoking" is a fact used to back up why he's chewing gum. It has no bearing other than to respond to why he's chewing gum. The perfect version wouldn't really work here because it usually stands independently as an announcement of sorts: [workmates]: A: You have good color - have you been in the sun? B: I've quit smoking))) I haven't touched a cigarette in two weeks and I feel like a million dollars. -Here the speaker is making an announcement about something that he considers a monumental change in his life.

This is where British and American usage part ways. In British English, the perfect can be used to state a fact (=our simple past) or to announce news (=our perfect). The two forms merge, so British speakers have to rely on intonation to indicate which is which.

I hope this isn't too confusing. Let me know if you have any questions or need me to clarify anything.

Uly, you're a great teacher. Thank you!

My pleasure, Alex)))

👍