Unless your theme uses some type of hook to add the logo, there is probably not a solution in functions.php. Your best bet is to look through the different PHP files in your theme to figure out where the logo is being added with no alt text. From there, ideally you would check to see whether your theme is housed in GitHub. If so, copy it, add the alt text the same way the homepage calls it, and submit a pull request to the author. If that’s beyond your skills, enter a bug instead. If it’s not in GitHub, contact the developer through other means and let them know. Once they fix it, you and anyone else using the theme will be able to benefit from the update.
If you want a quicker fix or aren’t able to get hold of the developer, you could create a child theme, copy only the problematic PHP file into the child theme, copy and paste the alt text the same way the homepage calls it, and you’d then just need to create a style.css file with a few comments identifying it as a child theme, then activate that theme.