This might be interesting if we switch to a CI-based build step later: https://phabricator.wikimedia.org/T199004#4436491
The comment T199004#5025574 makes a very good point: backports of our commits will be really tricky...
We would have to recompile typescript and vue on the production server, wouldn't we?
In conclusion: T199004: RFC: Add a frontend build step to skins/extensions to our deploy process is exactly what we want. But unfotunately, the discussion on that RFC seems to be far from finished and implementation will take even longer. There doesn't seem to be a way provided by Mediawiki or WMF for a dedicated frontend build step, neither in CI nor in deploy.
So we will have to roll our own build process for now. I understand this means doing the build locally and then checking in the files in dist/ ourselves. If we can find a nice CI solution later, then that might even contribute to the discussion in that RFC.