Updating from diffs is significantly more complicated when multiple diff sources are involved. I recommend you work out the PBF size by adding up all the country sizes on the download site and if it’s more than 10GB, go with all of Europe.
The guide you linked uses osm2pgsql replication. A better place to start would be the PyOsmium guide which would be useful as a reference, but do not try to follow it out of the box. This isn’t a “hacky” approach, it’s just lower level.
Broadly speaking, an update script needs to download the diffs, process the diffs, apply to the database, update its state, and handle expired tiles. You must write the script that does this.
You will need state files for each region you’re downloading, and you will download the diffs and merge them with osmium-tool. When that’s merged, you apply it to the database and only then update the state files locally. osm2pgsql can output the dirty tiles.