I've never actually heard any English speaking person refer to the Czech Republic as Czechia. https://www.theguardian.com/world/2016/oct/25/nobody-calls-it-czechia-czech-republic-new-fails-catch-on
You mean Čechy, Bohemia is obviously singular.
Čechy is even morphologically clearly formed as plural (the -y ending) and follows other plural country names such as Bavory (Bavaria), Franky (Franconia), Rakousy (Austria). Most of these are archaic today with the exception of Rakousy which is still used for the federal states of Lower and Upper Austria (the whole country is Rakousko). Franky is also still used as a Czech name of the historical region of Franconia. Another Austrian federal land is Korutany - Carinthia. Tyrolsko (Tyrolean) can also be called Tyroly. Italy had an archaic Czech name Vlachy.
I bet there will be more which I can't remember now. Oh yes, Flandry - Flanders which looks like plural in English as well.
So the reason is that it was customary in the old times to use plural.
Another ones: Burgundy (archaic), Uhry (pre WW1 Hungary). Very uncommon Bulhary, Kašuby.
Actually, it may be derived that way, but not simply from using one plural word for the country and for the inhabitants, but bu deriving the country name and changing to the inanimate plural suffix.
I found this:
Častý bývá ovšem i způsob opačný, že totiž jméno země tvoříme ze jména obyvatel. To se děje zpravidla příponou -sko: Rus - Rusko, Rumun - Rumunsko, Horák - Horácko; jednotlivě (a ve většině případů již archaisticky) plurálem jména obyvatelského: Španěl - Španěly, Švýcar - Švýcary, Prus - Prusy, Němec - do Němec. http://nase-rec.ujc.cas.cz/archiv.php?art=3346