Politicians, that is to say, the people that we elect, do not actually do the work of the government. Their primary job is raising funds and encouraging people to vote for them. Legislation is mostly written by their staff.

If a politician participates in writing legislation, it's not as a developer submitting changes to legislative review. It's as a manager, writing out a few lines of direction that do not work as actual law. The actual developers (staff) are then expected to fix that.

I doubt that most legislation writers use the same version control as is used for software. Unlike software, legislation is written in normal language. It has one hard line break per paragraph rather than one per statement. They are far more likely to use the revision control built into something like Microsoft Word. That is less about collaboration with a central source and more about seeing who made what changes when. It's also more consistent with how they've done it historically.

Programming benefits from having everyone involved familiar with computers. It's natural that it's on the cutting edge. Even with that, Git only dates to 2005 and Subversion to 2000 (source: Wikipedia). Older systems like SCCS and RCS only worked with changes by line, which as previously noted would have ended up being paragraphs in legislation.

Note that staff works full time on whatever legislation. They operate in small collaborative groups that actually can meet with each other to write legislation. In particular, in the United States, committees have their own staff that are true subject matter experts. You mention Europe, which may operate differently. But I suspect that it doesn't.

Legislation written in public in version control would be a great idea for transparency. Unfortunately, most politicians are more interested in getting reelected than transparency. You can see this in California (US), where there is a system allowing law changes by public referendum. Politicians are endlessly, albeit privately, complaining about how these make their jobs more difficult. So any progress towards transparency tends to be made in fits and starts by newer legislators.