Merkaz Harav has invited the Prime Minister to the Yom Yerushalayim celebrations for a long time. I dont know if they always did or only since Netanyahu has been Prime Minister. I tried finding information but couldnt really find anything solid. I know they invited Jerusalem mayors as well, and other politicians at times.

Even if they do not have to invite PM Bennett, I think it is a mistake not to, and it is definitely a mistake to invite the Head of Opposition without the Prime Minister. Meaning, if you are not going to invite the Prime Minister, dont invite Netanyahu either. Inviting Netanyahu and not Bennett turns the yeshiva too political and divisive and in the long run will likely be bad for the yeshiva and for Torah in general. Dont invite any politician is better than inviting just Netanyahu.