That’s not the tax dodge.

The foundation is its own 501c non profit, they donate to it, put their money into the trust fund.

The trust fund then turns and invests all that cash thst they donated and make bank while paying back “costs” for whatever. The only tax that gets paid is personal income taxes on the salaries paid out.

Which are much reduced because the fund also pays for things like hotels and rentals and travel

What the foundation then gives out, they were going to give out anyhow so as to whitewash their reputation and make themselves feel good

It's exactly how it works. You calculate what your tax bill will be, and instead of paying it in taxes where the government decides what to do with the money (in theory democratically, in practice it's different obviously, see point #6), it goes into a charity in your name.

Then you use this charity for multiple things:

• Free PR, as you don't need to use your own money, you use the money that otherwise went to taxes. The headline is X donates $N billion to charity, you look so giving, even though it's money you wouldn't have been able to keep any other way.
• Your foundation donates to prestigious academic institutions. That's something that you can parlay into a board seat or at least influence. Now you can decide what this institution will do. In Bill Gates' case, he used his influence to make sure the Oxford vaccine wasn't open sourced, but instead licensed. This delayed the response in the developing world by a year or so, and made sure that the pharmaceutical industry made even more money than they even made otherwise. Oh, and Bill Gates privately (on the non-charity side), owns a bunch of pharma stock.
• speaking of academic institutions: you buy a fancy building for their economics department. Suddenly the whole field of economics is basically limited to professors teaching trickle down economics. Marx' analysis of economics is considered fringe, and MMT as well.
• your foundation throws ~~parties~~ fundraisers where you get to hang out with important people. Catering, venue, entertainment, etc is paid for by your charity. The people donating to your charity are using their own charities to do so, it's just one big circlejerk with free money that would've gone to taxes instead.
• you get to circumcise a bunch of African men for dubious reasons and people will think you're awesome
• your foundation can donate to politicians or political organisations that will advocate for things you want. The things you want are deregulation, less taxes, etc. This in turn benefits you personally again on the non-charity side.

Just write it off!

They donate to their foundations. Their foundations are only required to use ~5% of their assets for actual charity.

Private foundations are required to spend annually a certain amount of money or property for charitable purposes, including grants to other charitable organizations. The amount that must be distributed annually is ascertained by computing the foundation’s distributable amount. The distributable amount is equal to the foundation’s minimum investment return with certain adjustments.

...

The minimum investment return for any private foundation is 5 percent of the excess of the combined fair market value of all assets of the foundation

These are actual IRS links.

So these foundations are free to invest 95% of the money into whatever they want and only 5% into charity. And this data is partially open, they invest into oil, pharma, finance etc.

What is not open but very likely happening, is private talks behind the scenes about what these 95% should be invested in based on personal motivations/goals of these billionaires, i.e. just doing with their money what they want anyway, just in a tax-free way.