Hey @iljapanic, here are some updates on your request:
@jr9000 has built a similar extension for the Baserow Developer Challenge. It could potentially be finished soon (so it will become possible to save data from boards directly to your Baserow tables).
We also plan to add this as a built-in feature in Baserow in the future. You can track the progress on this issue: Web clipper Chrome extension (#2437) · Issues · Baserow / baserow · GitLab