It’s still a ton of money to waste on a petty personal spat
Running for Senate allowed him to raise money through campaign finance rules, money that can then be applied to promoting the agenda through advertisements, travel, staff salaries etc.Not for a billionaire. This is pocket change. It also supports his competing product and attempts to move him into the national spotlight. He ran for US Senate in 2022. He even garnered 1.1% of the votes in California.
It doesn't have to be the case that he actually thought he had any chance to win, though for a person of his personality and delusions, anything is possible.