Type 51b is 6000+ ton ship where as type-54 tughrils are 4000+ ton. That's a big difference so you cannot say both are of comparable size at all.
Rest of your points are valid. It's correct that we still haven't seen P-282 and it might be PN type-54 (Tughrils) carry a different missile. But there have been reports in the past that they carry P-282.....but not confirmed. There are also reports that they carry YJ-12/CM-302. (though that leaves the question, why not P-282? Is it not available yet? Or is YJ-12 better?)
The assumptions about Babur class were not mine,,,,I was only replying to the defenceturk.net article posted above which made those statements. But you are right that the report might not be accurate. But that's why I asked the questions,,,,,, so we can discuss it. Any discussion needs a reference point