Google acts like I dont exist at times or lacks data to pull from

Long story short I am trying to find ways to google to have a reference or backlinks to call back to when pulling data for my website. today i corrected a few bad citations and stuff but wondering about backlinks. If I have backlinks out there and I am able to get them text on them fixed, or the surrounding text. Should i be adding NAPs to my backlinks at times as well. I am just guessing here but my informations seems to be all over the place and google is confused. Sometimes i can rank 1-3 organic then get dropped to page 2 and i think this is part of the reason why. Today on gemini my website does not exist..... as a example. I been cleaning up citations i found via site:searches.

Is there a list of things i can do or paritally do to lead the horse to water here?