Forgive me for being blunt, but what idea? If the question is who is supposed to fund Chromium and Firefox going forward then you haven't actually offered any ideas.
Commercial funding is not necessarily more reliable in general. Google keeps shutting down stuff all the time. But in this particular case, the commercial interest is so strong that funding is secure.
In my opinion, governments should focus on natural monopolies (taxation, violence, justice, transport infrastructure, water, etc) and on areas where there is broad consensus for a public option (health, schools, etc).
Where governments fund random stuff that few people understand the importance of, there is a big risk of the whole thing getting DOGEd or starved to stagnation. The government would never put up a fight against Apple relegating the web platform to the status of a glorified document viewer.
In my opinion, the status quo is flawed but the alternatives are worse.
If the court decides that Google must "divest" Chrome, they will have to say what that means for an open source project. If it basically comes down to Google being banned from controlling the default search engine setting in any web browser, then their main incentive for funding Chrome would be gone.
If that happens, the only solution I see is a joint "Chrome Foundation" effort funded by a number of corporations with a less direct interest in the viability of the web, i.e the Linux model. But this would be very disruptive. I fear that browser development would be aimless and start to stagnate. Other oligopolists would quickly take advantage of the ensuing power vacuum.
The government does not need to maintain a browser to enforce this rule. It would simply tell people that logging into the internet requires government ID now, and the ISPs would make it so or be shut down.
The government could however, if it maintained a browser, guarantee that the internet would be accessible without a government ID, just by not putting that feature in their browser. A government browser would be subject to the constitution, debate, public comment, and legislation; rather than having to sue companies to get anything done.
Google, Apple, and Mozilla are not protecting you from the government. They're intimately financially interconnected with each other, and can decide what the entire world is going to have to tolerate on the web on a group chat. Without government intervention (even if just to collect bribes), they'd all just probably merge and enslave the planet.
Maybeee the EU but we are talking about an American ruling.