Let's start with the type of batteries - I think they are wet since non wet sealed batteries (AGM, GEL etc) typically have a flat top with no visual way to open them.
I could not identify what this black round on top is - if it is some kind of a "window" these are probably "maintenance free" sealed wet batteries.
If you can you easily pry out the two rectangular tabs, these are regular wet batteries and this will expose the electrolyte openings and you should be able to see the top of the plates.
If these tabs seem to be "glued" or when removed no opening exposed then again - probably wet sealed type.
Testing - You could test while the batteries are in parallel, but they should anyhow be disconnected from all circuits, so disconnecting the link between them as well is no big deal. If any of them is in poor condition it will affect the second so in any case, whether tested together or separately both will have to be replaced as batteries in a bank must be identical.
Charge them fully.
Disconnect them and wait for several hours (24 hours is best but practically 3-4 hours will also work).
Check voltage - if it is 12.6-12.8 then they are good, at least in terms of being able to be fully charged. Any voltage below that means that they cannot be fully charged (or lost charge very fast during the 24 hours). every 0.2V lower means roughly 25% of charge lost.
Then, I would check voltage when they are connected to loads - turn on the fridge (I assume it consumes 4-5A, if you have a clamp meter you can check exact current) - voltage on the battery terminals should drop by no more than 0.1V.
My experience is that when the house batteries get old and charge less you notice it without doing too many tests, so if you did not notice any major change over time then they are probably OK and if you did they should probably be replaced. Nevertheless the above tests may give you a more "scientific" answer.
