Database and back-end (PHP) hosting tends to not be "forever free" in the same way as you might find things like github pages to host static (no database or backend) sites since databases and backend scripts requires more resources to host and organizations cant give those away for free as easily.
Some of the cheaper solutions like nearlyfreespeech.net are pretty close to free but that savings comes from the DIY nature of their service and having minimal support/no dedicated support team.
MongoDB Atlas may have a free tier you can use if you are okay with using a non-relational database. There also seems to be other options listed here but your mileage may vary.
Google Cloud, like many other large cloud providers, has a free tier program and $300 first-time-user credit that you could use, however these are designed to give you a taste of their services so you eventually upgrade and pay for the service and so the cloud providers may focus their efforts on paying customers rather than free-tier users or require you to upgrade for certain levels of support
Another option could be to package your software as a Docker container which can make hosting your app easier if you choose to self-host somewhere. Many cloud providers like google cloud and digital ocean offer hosting for these containers, however it is often more expensive to run as a service so this may only be a good option if you have a spare PC or existing server and want to host it yourself.
While you may be able to find free options from places like https://www.freemysqlhosting.net/ or one of the ones listed here, remember that these providers have to sustain themselves as a business too, so there may be ads, limitations, or failure of the business that can cost you more than if you paid for a service