Septic tank - problem?

Something's definitely off here!

I would speculate that the septic tank pre-dated the widening of the concrete - but cannot work out why, other than sloppy work, they would have concreted over and then put manhole covers that serve no purpose (other than perhaps to fool people into thinking the job was done right!)

[If I understand correctly, you open either manhole cover, and just see the same concrete immediately beneath it?]

Certainly, pretty much regardless of the type of tank, you need to be able to inspect it.  Soakaway types are not uncommon here, and are not as bad as they sound - and if they're working well, they shouldn't need emptying under normal use (= provided you're not putting loads more waste down the system than was envisaged when the tank was specified - and by the way, you'd need to minimise chemical-based products, bleach, etc, ideally using products labelled as septic tank suitable).

I suspect a plumber is unlikely to want to get into this (though some may).  Typically (but location-dependent) your municipal water supplier may be able to send someone, or recommend someone; or there will be one or more private septic tank companies (emptying, installation, etc) serving your area.  I'd speak to them.  

This may just be a question of access for inspection - the tank may be perfectly functional and adequate, if only you could get into it!

If it needs substituting, consider its location.  It's hard to be sure from the photos, but aside from being under a patio, it's relatively close to the house, and may be higher than and close to other features (pool, outdoor leisure space, cultivation).  Replacement, if required, should take into account current regulations; and all such water systems should technically be registered with the APA (Portuguese environment agency) though few legacy systems, and many new ones, aren't.

Posted by: @genki

concreted into the centre are rebar style handles

Were it not for the other bits you mention, this would make some sense - concrete tanks sometimes have concrete hatches with such handles, which is a pain, as they get stuck shut, are hard to grab and manoeuvre, etc...  We have a water storage tank with such a lid, and grit and growth having got in around the edge, it's stuck fast.  It is just possible yours did work and make sense when initially done - or it could be a flaw in someone's logic...  I feel for you, and wish I could provide a convincing explanation!

On the slow flow, we have the identical problem in an 80s ground floor bathroom (and it's unrelated to the septic tank in our case).  You may have done this already, but try a plumber's snake (get a good long but thin one - they're inexpensive) and also try a decent drain cleaner (Destop in a purple bottle, which says it has two doses, is the best I've found that is compatible with septic tanks - half the bottle, leave it an hour or two, then rinse with cold water).  It's quite possible this issue is inadequate drop on the pipe run, pipe joints being done incorrectly causing sticking points, and/or massive build-up.  Another thing - not to be combined, for risk of the Destop coming back up! - is to fill everything else, plugs in, and then release all at once.  It'll burp back, most likely, due to the air lock, but can help...

Back to the tank... it may well be best to try to bypass your old one, to a new tank - there are good ones available, and if it's installed properly and for you, it may take away the headaches.  Just not something one wants to have worry about, I know!