The issue regarding the basses that I mentioned to you is separate from all other problems. I am not a professional tuner, but the tuning is truly terrible, so make sure they do it starting from scratch—meaning first tuning the A 440 and then properly dividing the octave before bringing in the subsequent octaves. If the octave is divided incorrectly, you carry all the errors of the middle octave with you, and instead of tuning, you end up detuning the entire piano, as happened in your case.
Regarding the "chirping" you refer to, to me they seem like harmonics that are a bit too prominent. Perhaps it would be worth checking the strike point or whether the dampers completely release the strings, or if part of them continues to rub against the vibrating string... Paolo will correct me if I am talking nonsense.
As for the basses, however, if you feel they are too exaggerated, it probably concerns the positioning of the piano within the room; that is why I asked you if it was positioned in a corner. Ideally, it should be placed in the center of the width of a room, and far enough from the nearest wall, with the lid facing the longest part of the room. The problem is that often inside homes there are no concert halls (obviously! I might say) and especially in small rooms there are always listening problems. That is, there are frequencies that create standing waves called "Normals" or "Modes" which, because they are stationary, reinforce each other giving the impression of reverberation; obviously, if the room is very large, the modes concern very low frequencies that we probably wouldn't even touch with the piano, so the modes of your room would need to be studied starting from the three dimensions (length, width, and height) to be able to resolve this problem.
In corners, as I was telling you, problems with the accumulation of low frequencies normally occur, so it would be advisable to move the piano away from the proximity of the corner of the room, but this is not always possible... I imagine you have the piano in the living room or dining room; there will also be furniture. In this case, you can "contain" the problem by using bass traps. These are corner units made of sound-absorbing material, appropriately shaped to absorb low frequencies so as to contain the accumulation effect and thus limiting or canceling—if the situation is not terrible—this problem.
This is a bass trap:
Obviously, there are different types and colors. If you have white walls, you can find white bass traps that will coordinate with the color of your home and will be less "like a punch in the eye." If you cannot find them, it is possible to paint them with specific water-based colors that do not alter the open-cell effect of the sound absorber, which is necessary to absorb sound waves.