I curious - but how does a company legally prevents its employee from starting a competitor product given that the employee might have insider information?

They don't. If insider information is suspected, the company can sue, and then prove it in court. See Waymo.

This is infinitely better than automagically preventing employees from being employable after working for a specific company.

using a non-compete agreement [1] in the employment contract or as a condition for a severance package, etc.

May or may not be enforceable depending on a million different factors.

[1] https://en.wikipedia.org/wiki/Non-compete_clause

Since TeamViewer is a German company I looked up the rules for a non-compete clause in Germany (https://de.wikipedia.org/wiki/Wettbewerbsverbot#Nach_Beendig...):

1. It can only be valid for up to two years after your employment ends.

2. Your former employer has to continue to pay you at least half of your last salary during the non-compete time.

Point 2 is interesting. From the employer's point of view, it must effectively act as a high tax on non-compete clauses, still stopping short of an outright ban.

It can't. At least not in Germany... Have you ever read the story of SAP?

What is the story? Any links?