>>3893448>>3893512The E-M1X is pretty great but you can probably get away with an even cheaper body. E-M5 Mark III or E-M10 Mark IV might be good too.
I don't know much about MFT cameras though and I'd personally recommend an APS-C Nikon or Canon, they both have a ton of good APS-C bodies with huge used markets, and tons of telephoto lens options, also with huge used markets. Both DSLR and Mirrorless options although they're both known for their DSLRs.
Also as far as bodies go, look for stuff you'd need while out birding. Weather sealing, fast burst speed, ISO performance, shutter speed, battery life. My camera (D5500) is absolutely shit in every one of these aspects lol.
Honestly you can make virtually any camera work for birding. I've seen pros take phenomenal bird photos with the Sony a7iii. And I've seen excellent photos with "entry-level" Nikon d3100s. It just boils down to how budget-minded you are.