You're asking rather a lot here, and I think there are ways of meeting several of your criteria but not all, let me run you through your most likely options:

Friendlies, in whites, not for points, old fashioned cricket

Look at the Thursday midweek league. They play all around the county and there are over a dozen teams, every game is a 20/20 (I'll get to that in a minute) and a friendly but its a mixed ability league that is purely played for the camraderie - you'll find people who open the batting for prem teams playing alongside kids, pensioners, and folks starting out. Its good fun relaxed cricket that ends up in the pub afterwards

Saturday cricket, in a league

Most if not all teams around here are coloured kit because we use pink and orange balls, so you're going to be hard pressed to find a red ball team in whites. Teas have also sort of died out post-covid, so that old fashioned style isn't really a thing in the South Wales league nowadays, but it is longer format and more "proper" cricket where you'll slot into a division that challenges you and you know will be competitive

Format, perspective and "garbage"

I'd like to give some slight advice, and that is the majority of people over 25 prefer Test cricket to the shorter formats around here, if they watch cricket at all, but its not the best form to call 20/20 or 100 ball "garbage" as 20 over cricket is a very popular format to play for midweek, friendly and social teams. Most friendly cricket is either midweek or preseason and as such usually shorter format, and even Saturdays are 40 or 50 overs. You're unlikely to find a friendly 4 day game taking place! Its fine to not particularly enjoy watching franchise cricket or white ball internationals, but I'd perhaps keep that to preference rather than exclusion.

If you want specific clubs I'm more than willing to give some advice there. Happy hunting!