Nobody is managing a big corporation because he cared about keeping his name on Santa's "nice" list. The donations that big corps do make are carefully calculated performative virtue - aka marketing - which they make only if, when, and where they feel confident of a positive ROI.
Or, very occasionally they are de facto buying software support with "donations".
It's not quite that simple because you are spending "other people's money".
Say I own a small business. I can make a donation to anything i like because the only person who might complain is me. Ultimately I am donating my own money.
If I work at a large company, all the money belongs to other people. Naturally I need to spend money to get stuff done, I'm given a budget and some rules framework.
To avoid corruption, theft and embezzlement, that set of rules has balances. People who audit my spending etc.
Imagine they set a rule saying I can spend $100k on "random open source". Cool, my wife makes an Open Source flappy birds clone. 100k to her.
Not cool, it must be something we use. Cool. My wife has forked a text editor (say emacs), made a couple spelling changes, and I've mandated that as our one-true-editor. 100k to her.
You get the picture. Donations are indistinguishable from corruption.
As a company what I want is for you to -sell- me something I can justify. Not just "the same thing under a different license" which spawns the "why aren't we using the free one" conversation, but some feature or benefit I can point to. We're spending 100k, but we got the following economic benefit from that.
So to answer your question. Companies can't "give", they can only "buy". (For any significant amount.) If you want corporate money, have a product to sell, and a proper process (invoicing etc) to process sales.
"Hey, Boss, I want to spend money on something that we already have. The benefits that spending will return are conditional, probabilistic, and long term, if any."
Its not an easy sell.
Several people have done fine work in providing example sales pitches, articulating the benefits of supporting open source generally and maintainers specifically. Even with that kind of help, it's still a hard sell.
Many business are run for today with no regard for tomorrow, stiff suppliers and contractors and come back next quarter whining about "but if you won't extend more credit you'll be taking hundreds of jobs!" Actual legal obligations don't mean much to those people; they'll never care about a commonwealth.
The better type of business still has far more things to do with their money than care for an apparently healthy and vibrant common ecosystem. Usually, the best they can do some public relations spending on par with the rest of their charity work.
I’ve never had a budget for donations as an engineer. That money would go through some other part of the organization.
I have had discretionary budgets many many times. I could easily give part of that budget to open source maintainers but I’ve also never found one that made it easy to get an invoice.
Can you expand on what "easy to get an invoice" means? What are the minimum requirements for what counts as an invoice? Specific formatting? A legal entity/business?
I think (self-employed, not from the US) that it needs to be a registered business entity (e.g. LLC) to give out invoices. Most of it has to do with taxes and regulations surrounding embezzlement/money laundering, Anytime you spend money as a business, that transaction needs to be accounted for, usually by more than two entities (you and your bank).
And yes, the invoice needs to have the information needed to identify both parties (business id/tax number).
If it ain't broke, don't fix it. If the software is ok and it's free, why throw money at it? Companies generally spend as little money as possible. The tech industry in the past 10 years was an aberration, because it was fueled by cheap VC money who see tech as "winner take all" market (which means that, if you outspend your competition, you will eventually end up with a money-printing monopoly). Hence, the $400k packages for individual contributors.
In general companies won't pay people to do things when they are willing to do it for free. There are exceptions. Linus Torvalds is paid by the Linux Foundation, which is funded by big corporations https://www.linuxfoundation.org/about/members .
They do, but indirectly. They pay Red Hat (RHEL) or SuSE or another commercial vendor for support. That vendor then hires programmers who contribute patches back to the Linux kernel and user space apps. For critical projects, they hire core team members.
Because there are hordes of neckbearded zealots who will loudly claim that's a Jeffrey Epstein level of immoral, and nobody benefits from that kind of distraction.
Or, to put it another way, because when you do that it is, by definition, no longer open source.
To be clear, this model exists, and is adopted by lots of startups and OSS companies when they decide revenue is necessary. But at that point they are no longer OSS and typically their very customer base, who have been selected because they care about OSS defect.
A golf club attracts members who want to play golf. Tennis is more profitable so they bulldoze the golf course and build tennis courts. Don't expect the current members, who were there to play golf to hang around.
If you are starting a business I encourage you to figure out the revenue model first, not as an afterthought. Hint "getting lots of users" is not a revenue model.
There are a few more examples in addition to Target over at https://fossfunders.com. There is a spectrum of approaches, but it's encouraging to see some companies willing to give financial support without necessarily expecting support or services in return.
In my experience (~10 companies, including bigger tech and silicon valley companies) the bigger the size the lower (if not zero) the awareness. In smaller companies and startup I've seen much more "empathy" and we used to give one-shot or recurrent sponsorship especially to projects that we were using extensively. This could also be a partial answer though, bigger companies don't really care as they could afford (or perceive so at the higher level in the ladder) to just move away or fork the project and maintain it themselves, thing that I've also seen applied in a famous telecommunication API company (guess who).
Or, very occasionally they are de facto buying software support with "donations".