[Task] Replace usages of `runCatching/mapCatching` with our own versions

[jmartinesp]

We're extensively using runCatching in the codebase because it's very useful, but it's also a code smell (see Kotlin/kotlinx.coroutines#1814). This can catch and ignore:

• Error types that should be thrown (see Stronger lambda error #4771).
• Coroutine cancellations that are needed to make sure the async code works as expected.

We should replace those usages with our own versions, maybe using some of the suggestions in the issue from the Kotlin repo.