@Zachary Rosa You are asking two different questions, "I bought the house for $700k and believe it is work much more and want to do a cash out refinance. I know commercial properties are valued based on the income. Is there anyone who will lend on an STR/residential property based on the income?".
First question, "I bought the house for $700k and believe it is work much more...". The house will be appraised as an SFR and that is what the bank will value it at. What it is worth to someone with a particular interest in it may be entirely different than what a bank will appraise it for, think of small poor quality houses that have been rezoned to commercial, the bank will value these as is while an investor may look at it as what they could turn it into.
Second question, "Is there anyone who will lend on an STR/residential property based on the income?". Maybe, I believe a DSCR loan will look at the income vs PITI and base their refinance on those numbers. I would search on these forums for DSCR loans and read up on it. I would also look for the responses that are actually informational vs "DM me". (caveat with that, one can only be generically informational without running afoul of self promotion rules. If all the person ever posts is "DM me", personally, I view them as looking for business vs trying to help)
I hope you find the answers!