But....how would that buy you influence? Unless Trump is selling stock, buying stock doesn't put any money in his pocket.

Buying shares of DJT could potentially allow for influence over Donald Trump in a few key ways:

Foreign investors could influence the stock price through large purchases or sales, knowing that fluctuations in DJT's value would have a direct impact on Trump's personal wealth.
This could be used as leverage to influence policy decisions.

Foreign investors or governments could attempt to curry favor with Trump by investing heavily in DJT stock. If Putin owned 35% of DJT will Trump pick up the phone when he calls?
A major shareholder can strongly influence a company. (See: Carl Icahn.)

Trump is set to receive additional shares based on DJT's stock performance over time. Foreign entities could time their investments to help Trump reach these milestones.

Finally you are 100% correct: Foreign governments could spend large sums on advertising on Truth Social or enter into lucrative partnerships with Trump Media & Technology Group.
This would boost the company's revenue and stock price, benefiting Trump.

Of course Putin, Xi, or Iran could also just make donations to Trump in untraceable crypto, which he is currently accepting.
Or they could just buy all of Trumps watches and sneakers.
Or they could just invest large sums into World Liberty Financial, Trump's cryptocurrency venture.
There are many avenues for Trump to be bought. Emoluments Clause you will be missed!