Several things:
Trump certainly wanted more. You don't sign a 2.2 trillion package in March and a 900 billion package in December if you don't want more overall. He signed both bills. No reason to avoid the obvious.
Trump and Republicans agreed on how much money they would support as direct payments. When the legislation was written, Trump backstabbed them and suddenly demanded more money. He did that for the publicity. (Notice he backed off almost immediately after "threatening not to sign" the legislation. He certainly didn't fight for it. Almost as soon as he demanded it- and it made news- he backed off. It was just a gimmick.
Did you need a stimulus payment? I certainly didn't.
What he should have lobbied for was increased payments to individuals that had applied for unemployment and were out of a job, not direct payments to all Americans. That is what some Republicans like Richard Shelby proposed. Giving money to everyone was just a vote buying gimmick for everyone involved. .
Trump directly lobbied for money to go to his some of his own businesses by making them eligible. Congress refused to insert it - angering Trump.
I didn't need a stimulus payment, and I didn't receive any of them. But the income limited were set by Pelosi in the House and they refused to change them. Dems loaded these bill with pork and refused to remove most of it. They took advantage of COVID to line their own pockets and buy votes. Period. Trump either had to sign it or let people suffer, and he didn't have weeks or months to fight with them over it.
And the crap about Trump wanting money for his own businesses is just that, crap. Dems wrote the rule that nobody in the Congress or White House could apply for the help because they wanted to hurt his businesses and employees. Anybody that legally met the rules and criteria should have been eligible.
Of courses, Dems never write that kind of verbiage into their own bills, despite blatant conflicts of interest. That should tell you something.