Upgrade TypeScript, unified watcher setup

[simolus3]

Blocked on #958.

When working on internal SDK changes in common, it's convenient to be able to see what needs to be changed in the individual SDK packages consuming that. Right now though, that process requires rebuilding every package in this repository, which is very slow.

In the PowerSync service, one can simply run pnpm watch:ts to run tsc everytime something changes, which is much faster than having to invoke rollup on every package. Packages still have their complex build logic, but running TypeScript is the first step of that. In the future, I hope we get to make it the only step for most packages, but we're not really there yet.

This also upgrades to TypeScript version 6. I mainly had to change a few catch blocks which correctly use an unknown type by default (but we can change that to any). We also a few packages opting in to strict type checks without really having save code - I've added ! assertions to keep existing semantics. Finally, resolving types in vue and nuxt is beyond broken for reasons I don't understand (it looks like types are resolved against @powersync/common/dist while symbols are resolved against @powersync/common/lib??). A few as any fix this, when we split common into interfaces and implementation we should be able to fix this properly.

[changeset-bot]

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