I will list a few points here that I noticed in FM23 and in some cases even in the years before. If I think of more, I'll add them to the first post.
1. If you have already offered a contract to a player you want to buy and then want to improve it, because you can see, that he has also received offers from better clubs, you can give him more money but you cannot upgrade the role promised to him, e.g. regular starter to important player.
2. If you invite a player without a contract, who has already received one or more contract offers from other clubs, to a trial session, he will always sign directly with one of these clubs afterwards.
3. in real life, there are many players every year, who have an uncertain future up to 1-2 months before the end of their contract or beyond. e.g. firmino and skriniar whose contract expired and they signed for new clubs after the end of the contract
In FM all these players have all extended their contracts with their clubs by november at the latest and there is no chance of a good player on a free transfer