[Tenant, US, CA] Garage Door Liability

Hi all - In my previous post, I described garage issue, due to normal wear and tear, I was having with my landlord (previous post linked). We kept going back and forth on who would pay for the garage repairs for a couple of weeks without any significant progress.

We had 3 repair options that I found through contractors I contacted since it seemed like there was no action on the landlord's part - replace the whole door, replace a section of the door, or fix/replace broken parts.

In order to resolve this issue quickly, I offered to pay for the repairs if we chose the fix/replace broken parts option (it was the cheapest and fastest). The landlord agreed to the fix/replace broken parts option.

Since then, it seems like the landlord has been trying to defer all liability and responsibility onto us - saying he won't be there to oversee the repairs since it's our responsibility, telling us that whether or not we listen to the contractor's opinion is up to us but he won't be involved in the decision making, and claiming we are responsible for garage maintenance.

Obviously, I do not agree that we are responsible for the garage maintenance or that we are liable for anything other than using the door properly and maintaining a clean environment.

My question is, despite my landlord saying we are liable/responsible for the garage door, would we be protected by the lease agreement? I do not see anything on the lease that says we are responsible for garage maintenance. And should I continue with the repairs or speak with the landlord about my liability before proceeding?

Here is the maintenance section of my lease:

MAINTENANCE USE AND REPORTING:

A. Tenant shall properly use, operate and safeguard Premises, including if applicable, any landscaping, furniture, furnishings, and appliances, and all mechanical, electrical, has and plumbing fixtures, carbon monoxide detector(s) and smoke alarms, and keep them and the Premises clean, sanitary and well ventilated. Tenant shall be responsible for any additional phone lines beyond the one line and jack that Housing Provider shall provide and maintain. Tenant shall replace any burned out or malfunctioning light bulbs. Tenant shall immediately notify Housing Provider, in writing, of any problem, malfunction or damage with any item including carbon monoxide detector(s) and smoke alarms on the property. Tenant shall be charged for all repairs or replacements caused by Tenant, pets, guests or licensees of Tenant, excluding ordinary wear and tear. Tenant shall be charged for all damage to Premises as a result of failure to report a problem in a timely manner. Tenant shall be charged for repair of drain blockages or stoppages, unless caused by defective plumbing parts or tree roots invading sewer lines.

(there are a few more sections but none are related to garage or appliances)