For your first season it is unlikely that they will be dried suitably (or at least for the beginning of the winter), so you might want to buy some in... for this year... Get some this summer, split, stacked to dry ready for next winter (2026-27), and you should be away.
Similar to Stubby, put a listing on the tip sites, and click the button 'Happy to pay' - it might make your site stand out from others around you... That doesn't mean you'll be paying for all your logs though, some people are happy to tip for free (the finances can make that work, less driving for them, perhaps a shorter day, or no second day on the job with local tipping, no council tip fees and so on).
If you are new to wood burners don't get hung up about 'kiln dried oak' only - all wood burns, even softwoods.
Back to the local firms - the more you can do yourself, the less they need to do, the happier they will be to tip. Some people are set up at home with saws, axes, splitters (plus safety kit), some don't - if you are happy to cut and split wood (can be therapeutic hitting things with an axe) - you'll get more.
For the tip sites, note that anyone local to you will probably have tip arrangements in place, people they know, a yard or whatever, but those working locally to you but from outside their usual area are more likely to look for a tip site... but there will will fewer working in your are - so don't expect your drive to be full of logs 52 weeks of the year (I reckon I get 1 or 2 loads a year).
One good thing about tree surgeons is they typically have a liveried van with a phone number on, are not quiet when they are working, you can spot them driving about - take a note of the number and give them a call direct (try to avoid times they are up a tree!) - that can work, or at least make an introduction. Likewise a lunchtime / morning cuppa walk can locate any chainsaws working within earshot (not quiet things)... divert your walk in their direction - can see who it is from their van, and if you get a chance a friendly "do you have somewhere to tip that" might also get results.