Watching some of the Beast in the East, I'm interested in playing 0, but I worry that it would be tough to go back to the older games (1-5). Do they hold up or should I consider going in release order?

I played 3 then dead souls and 4 about the same time. I have since got yakuza 1 for the ps2 and played a wee bit of that and it seems ok. Ive started Yakuza 0 but not played it much. I think 0 may be a good one to start with as it is a prequel and maybe get the 1 and 2 remake thats coming out after that then do 3 then 4.

If you aren't going to go back to the PS2 games I'd say 0 is the best place to hop on. No prior knowledge required, ties into and enhances the plot of 1 which there's a remake of coming this summer.

I played them all in order (minus Dead Souls and the other spin offs that didnt get localised) and i'd say yes. The combat in the first game is sluggish (even at the time) and the second game while maybe having the best storyline isnt required to understand what goes on in the later games. Also as far as I know Kiwami (the remake of the original) doesnt do anything crazy like Twin Snakes so playing that you will get more or less the best version of that story. (I say more or less because the english voice acting is hilariously bad in the original)

A lot of the mechanics in Yakuza 0 feel archaic already. Yakuza 0, from a gameplay perspective, is as smooth as it has ever been so going in release order might deter you all together from Yakuza. Each Yakuza game adds on and smooths out mechanics but roughly each game carries the same structure. As you've seen from videos, Yakuza is a brawler where you level up your character in an interactive open world with quirky side quests and a dramatic main narrative. It has always been this. The narrative is often engrossing, the combat is serviceable, and the side quests are one off entertaining filler. Mostly, the one thing they are always adding are the mini games (arcade games, batting cages, karaoke).

Either start with Yakuza 0, and if by the end want more Yakuza, look into getting the first game. Or start with the remake of the first game that is coming out and then go release order. That's my two cents.

The only one I'd have bother with is the first one. It's a stiffer experience and they tend to add and refine game upon game. 0's a good starting point and, should you move to 2, 3 or 4? after that, they all contain catch-up videos that explain years of .... stuff.

I am starting with beast in the east, if they remake all of them i may just go in order from there.

Play them from 1-5 first, or at least start from 3 and watch the recap videos. You needn't even play Yakuza 0, since 1 is more revelatory about Kiryu's backstory than 0.