My name is Mika and with a couple of friends we have developed www.gameswap.io where users easily can get information where they can among other things borrow console games. Right now we are getting started in Sweden where we have connected with the National Library of Swedens API LIBRIS. Currently not all of the data is visualized but users can sign up and create lists of games they are looking and get notified if/or when they are available at any library. My question to you is if there is a similar API available for Finnish Libraries where we can get information about what games are at which libraries in Finland?
If i understood correctly, you are searching for a possibility to find materials, especially games, in every (public) libraries in one "catalogue". There is Finna.fi, which contains a great part of Finnish library materials, but not quite all of it yet. You can see how Finna looks like here, https://finna.fi/. Finna has an own developers-Wiki, https://www.kiwi.fi/display/Finna/Finna Maybe you can find the information you need there, or at least contact persons. You can send mail to email@example.com.
An other way to find library materials in one search is the metasearch of Kirjastot.fi, https://monihaku.kirjastot.fi/fi/. Here the problem is that since the metasearch searches on different databases with different kinds of solutions in description, the same material can have different kind of material types or keywords. But this can be a problem in Finna too.
I good idea might be to ask this blogger who writes about Games and their use in libraries https://www.kirjastot.fi/pelit. If there is a third alternative, he is the person, you could know about it.