fix: raise errors on invalid inits, failed integrations, etc.

[beckermr]

As it says above...

[codspeed-hq]

Merging this PR will not alter performance

⚠️ Unknown Walltime execution environment detected

Using the Walltime instrument on standard Hosted Runners will lead to inconsistent data.

For the most accurate results, we recommend using CodSpeed Macro Runners: bare-metal machines fine-tuned for performance measurement consistency.

✅ 36 untouched benchmarks

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_{Comparing equinox-err-2 (24f1ccf) with main (f6ed18a)}

[beckermr]

Ok this one is ready for an initial look @ismael-mendoza. I expect we may iterate a bit on this one.

[ismael-mendoza]

Thanks Matt! I only have a few minor comments

[beckermr]

@ismael-mendoza This one is ready for another look!

[ismael-mendoza]

Looks good!