Make FlexiChains the default chain type

[penelopeysm]

Mostly interested in seeing what breaks, I ran some tests offline then got bored.

As far as source code changes go, I only needed to change the definition of DEFAULT_CHAIN_TYPE and twiddle with some imports. So in principle this is pretty much done.

Most changes were really in the test suite, using chn[@varname(x)] instead of chn[:x]. In fact, that isn't even necessary, but I just consider it good practice.

The only changes that I found to be mandatory were changing things like chn[Symbol("m[1]")] to chn[@varname(m[1])], which is a Positive Change, and also other things that relied too heavily on the exact internal structure of MCMCChains, which is also a Positive Change, or a Neutral Change in the cases where I had to rely on the internal structure of FlexiChains.

This PR should definitely target breaking, but that would cause version conflicts with FlexiChains, since FlexiChains has a compat entry that pins Turing to its current minor version. That can be fixed by moving FlexiChainsTuringExt into Turing proper, so that that compat entry can be removed.

[github-actions]

Turing.jl documentation for PR #2743 is available at:
https://TuringLang.github.io/Turing.jl/previews/PR2743/

[codecov]

Codecov Report

❌ Patch coverage is 16.66667% with 15 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.61%. Comparing base (6df73f8) to head (7787790).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
ext/TuringMCMCChainsExt.jl	0.00%	15 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2743      +/-   ##
==========================================
- Coverage   85.40%   84.61%   -0.80%     
==========================================
  Files          22       23       +1     
  Lines        1501     1514      +13     
==========================================
- Hits         1282     1281       -1     
- Misses        219      233      +14     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[sunxd3]

LG! (it is breaking indeed)

[penelopeysm]

Thanks @sunxd3! Yeah, it is actually even more work than this. I need to transfer the extensions into Turing/DynamicPPL as well. That should hopefully just be a copypaste but I'm sure it will break something...

[penelopeysm]

I probably won't have the time to finish this up.

(well, it seems it depends on whether I want to work on the weekend lol.)

Sequence of events:

• Release a version of FlexiChains without Turing compat Remove Turing ext penelopeysm/FlexiChains.jl#193
• Release this version of Turing
• Update Turing docs