A6:

In Czech Republic it is bit mess with the bike options so I will explain more:

Regional trains are subsidised by regional governments that picks the companies that will run the trains on specific lines and decides on priorities. So you can end up in Arriva carriages that are old German suburban trains without much bike spaces (still possible to take your bike there). In my region they bought new RegioPanther trains with space for 8-20 bikes (depends on line) but they don't mind if people just completely stuff the compartment if there is demand. Older trains have place for at least 8 bikes in multiple places on the train.

On long route trains it really depends on the company that runs the trains - ČD, ÖBB, Slovaks and Magyars have some spots for bikes but usually you have to reserv a spot (it's not that necessary if you know how to get around, which lines to take...)

Student Agency, Leo express and other private companies usually don't offer bike spaces.

It sounds complicated (and it is) but when you know what you are doing it is easy and doable. Also the tickets are quite cheap - bike costs in my region 1,5€ and for long trains ~5€ (depends on the route).

I posted a picture 1y ago on Lemmy from older train:
sopuli.xyz/pictrs/image/63a9bf…

if you need some more tips about trains or where to ride you can reach me here 😉

I have some experience with bike& train travel from Austria, Germany and Slovakia to Czech Republic and lots of long routes riden here (mostly west and south Bohemia and south/central Moravia).