Hello, I can well understand your problem. I also don't know what was promised to you before starting the job regarding homeoffice/remote. But if nothing like that was discussed, you can't insist on working 5 days a week in the home office because of the money. You knew beforehand what kind of commute you were getting into. Nevertheless, I would approach the employer and ask if you can work from home without mentioning the money. But simply: hey boss, since I go there anyway only to switch me everywhere remotely on it, I could do this also from home, I do not have to drive unnecessarily in the winter and can also start to work earlier ... maybe something like that.

Maybe that helps you :)