Does fasting become invalid if one believes that they have broken their fast due to the devilish whisper that water entered the stomach during ablution, and not spitting out the water from rinsing the mouth after having already spat?

The cure for obsessive thoughts (waswas) is to ignore them and pay them no attention. Your disregard of remembering your fast does not affect the validity of your fast, as long as you did not firmly decide to break your intention of fasting. Firmly deciding to break the intention is among the things that invalidate the fast, unless it is due to overwhelming obsessive thoughts. Swallowing water during rinsing the mouth (madmadah) does not invalidate the fast unless you are certain it reached your throat. Swallowing saliva mixed with the moisture from rinsing does not harm, unlike intentionally swallowing water.