While linking new project created on user account to single billing account, getting quota error. Already 3 project linked to it and not allowing 4th one.
Try restarting your browser–to ensure that no incognito windows in the background are logged into any other Google account–and then logging onto your administrative account in a new incognito web browser window.
Then go to your trial billing account and look at what projects you have attached to it. You’ll probably have at least your billing export project (which you should keep) and some sort of "My User Project" that was auto-created for your administrative user. That latter one you can probably delete, if you’ve not used it. But if you’re not yet sure about deleting that project, it is also fine to just unlink it from billing, for now. Either way, that will give your trial billing account a bit more linking quota that you can use for your "Services Exploration Labs" project with your user account.