All major browsers support redirects and have done so seamlessly for 20 years.
The last browser that didn't support redirects well was Netscape 4. That was about 1997. Even then, redirects worked but:
- The screen would flash.
- The redirect URL was added to history. That meant that it was difficult to use the back button from the page after the redirect. Users would have to hit the back button twice really quick or they would end up just getting the redirect again.
Normally when you have questions about whether browsers support a feature you can can consult https://caniuse.com/. However, redirects have worked well for so long, that they don't feel that it is a browser feature even worth covering.
Redirecting to include parameters is fully supported as well. Your example redirect will work as you intend in all modern browsers.
Even though redirects work really well, they probably are not the correct solution to your particular problem. Ideally your login form would be produced by the same PHP file that checks the credentials. This would allow you to show the form again with the error message without doing any redirects. Typically redirects are use after sucessfulsuccessful login to take the user to whatever page they need to see next after logging in.