There isn’t a way to access the Webflow CMS API directly from client-side script, so you need a middle-tier.
If you’re comfortable with Javascript and forms, and only need to update one record at a time, Logic is a good option here. You’d pass your data into a hidden form and submit it, and Logic would take over.
There are a lot of popular 3rd party automation services as well like Make.com that can perform CMS updates.