That train isn't running since 2020 and last December they have announced that won't be coming back for the foreseeable future.

Really? Oh no :( I never got a chance to take it, from what I heard it was a fun experience.

IRE trains are extremely rare. They have never been a regular product, but results of local political bargaining after the popular IR trains were discontinued ages ago.

There is a RE from Hamburg to Berlin?

No, RE stands for 'Regional Express'. There is RE between Hamburg and Bargteheide for example, but Berlin is too far away. REs are rather for commuters from nearby towns.

No you have to switch trains at least once.

Also the travel takes ~4h15m (RE->RE) instead of ~1h50m (ICE).

If your traveling at a time where the RE is not over crowded and you can spend the time well it's okay. If not, especially if the train is overcrowded in parts of the travel and it's really hot it's shit.

There used to be an IRE, which stands for inter-regio-express. But apparently it was discontinued during covid.