Refactor test suite

[lkdvos]

This PR separates out some of the parts of the test suite in order to increase parallelism on the github runners, and get slightly better feedback on where things went wrong if they did.

The main idea is to organize the tests into groups, as dictated by a folder structure, and then the QuantumKitHubActions workflow takes care of the rest. Additionally, you can control them from the local command line through:

import Pkg
Pkg.test("TensorKit"; test_args=["--groups", "other", "symmetries"]

which would run only the other/ and symmetries/ tests.

I've made sure that the individual files are all self-contained as well, so a workflow like this also works:

using TestEnv; TestEnv.activate()
include("test/symmetries/fusiontrees.jl")

Obviously the split I chose is arbitrary, and I'm happy to rethink all of the names.

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This also tackles some issues we had with the CompatCheck workflow
This also fixes a breaking change we accidentally slipped in with the TensorKitSectors v0.3.1 changes.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

🚀 New features to boost your workflow:

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

[lkdvos]

Had to patch the parsing due to QuantumKitHub/TensorKitSectors.jl#32

[Jutho]

Thanks for this; this looks great. I left a few small comments.

[lkdvos]

I think all comments have been addressed here, all this needs is an approval and it should merge as soon as the tests pass.