I love Sly Cooper and I really want to run the entire series but I personally can not get my hands on a physical copy of Sly 1, 2 and 3 but I do have PS Plus on PS5 which recently made available the Sly Collection and Sly 4. Would my runs be accepted if I run them on there and of course following all the rules previously stated

If you submit your runs under the PSNow platform (and the hard drive submitted based on your system's hard drive), you will be totally fine to submit a run on the leaderboards. Though it is not the fastest version, it is still allowed for the leaderboards as its an official means to play the game(s).