Help needed - how to file a damage claim against a home warranty contractor??

Here's the situation - we're in the first year of owning an older home (TX) and it came with a home warranty, so as terrible as they're known to be, we've been trying to use it to get a faulty dishwasher repaired or replaced.

Yesterday, an appliance repair technician (assigned through a home warranty claim) came and made an attempt to repair the dishwasher. He replaced a part, but then said it needed a new water supply line, and this meant transferring the service request over to a plumber. He turned off the hot water supply under the sink (the dishwasher supply feeds off this spigot) until the plumber visit could be scheduled, BUT the water wasn't completely off and it turns out the water line he re-attached to the dishwasher wasn't fully sealed so overnight the fitting on the dishwasher leaked and caused a small flood under the washer which has saturated the wooden floor under our kitchen floor tiles. I have videos and photos of the leak, the flood, the wet tile grout etc, but I don't know what my best course of action is..?

From what I understand, the home warranty company will deny all responsibility and pass it onto the contractor.

The contractor is only a name and phone number to me - there is no more info on the home warranty service request and I cannot find them online (I'm going to do a search of the TX state business database, just haven't got there yet).

If there ends up being severe damage to the kitchen floor and tiles, it will be a significant cost to remedy. My instinct at the moment is to do the following:

- lodge a complaint/claim with the home warranty company just so it's on record.

- find more company details for the contractor and submit a written letter of complaint and notify them I am holding them accountable and will filing in small claims court for any damages,

- notify my insurance company as they might take action against the contractor to avoid covering the claim themselves.

Any assistance, guidance from similar experiences or 'insider' industry info would be very much appreciated.