Improve performance of depth-limited type printing

[charleskawczynski]

This is an attempt to close #55952.

[LilithHafner]

FYI it might be hard to find a reviewer for this PR as it is a large diff designed to improve performance in displaying types that have size on the order of 1 million which is not a particularly high priority area afaict. You might want to seek out a reviewer on slack and include stronger justification in the OP of the PR.

[charleskawczynski]

FYI it might be hard to find a reviewer for this PR as it is a large diff designed to improve performance in displaying types that have size on the order of 1 million which is not a particularly high priority area afaict.

I've seen stack traces ClimaLand whose frames take ~2 seconds to print, leading to traces that take tens of seconds on every error.

You might want to seek out a reviewer on slack and include stronger justification in the OP of the PR.

I already tried that, but nobody has responded:

Hearing "not a particularly high priority area afaict" is very discouraging as a Julia user. And folks at CliMA, myself included, have really struggled with some aspects of Julia and it's tooling.

For example: JuliaDebug/Cthulhu.jl#566 (comment).

I'm going to mark this PR as a draft for now since it's not yet ready for review (I've realized that my proposed solution in the issue is not sufficient for the context of how Base's show works).

[LilithHafner]

Thanks for marking as a draft. When it is ready for review you can ping me and I'll try to help find someone (but no guarantees). Maybe someone at SciML will help review this.