Fix TS example for recording exceptions

[Grunet]

Resolves #5805

I tested in the Typescript playground that this fixes the type checking issue.

I have not checked that this fully functionally works (is there an existing otel-js playground for that? If not I can probably find an online editor playground to setup in. Just lmk)

[theletterf]

@open-telemetry/javascript-approvers please have a look — thanks!

[pichlermarc]

This looks good, thanks 🙂

@Grunet I'm not aware of a playground to try things like this, but I checked that locally when I suggested it over at #5085. That's also the way we do it in some OTel instrumentations so I'm confident that this is the correct way to do it. 👍

Functionally, there's a difference to what it did before as it won't record anything that's not an error (recordException would technically allow for custom types that roughly match Error, and strings too), but I think this check covers the vast majority of cases. If users need to record something other than Error then it's still possible to check up on the type-defintion of Span#recordException() but I don't think it needs to be spelled out in the docs :)

[svrnm]

thanks @Grunet ! For testing/making sure that the code works we want to roll out a "code excerpt" solution long term, until then we appreciate if people test their work locally and provide it afterwards.

[cartermp]

I tested this and it looks good. Thanks!