Playstation , xbox on 120 watt inverter?

OK so I have a 120 watt cig outlet with a 15 amp fuse. I am trying to run a ps4 slim or xbox series s on it. So far I have blown over 10 15amp fuses. This is my inverter -

BESTEK 300W Power Inverter DC 12V to 110V AC Car Inverter with 4.2A Dual USB Car Adapter https://a.co/d/86fzbfL

I was sad today because the xbox series s which says has an average draw of 70 watts blew the fuse and I'm trying to find a solution. I am starting to guess that the enclosed space might be forcing the xbox to use a lot more power for cooling but I have my doubts.

Should I perhaps switch from the 300 watt to 120 watt inverter to protect the electronxics? What happens if more power is drawn - does the inverter just stop? Should I try and get a pure sine wave inverter?

 

I'm thinking of getting a power station like this so that I can have atleast 300wh of backup for safety. I do want the power station to keep charging though. How do I know that the power station will only take less than 120 watts from the cig lighter as I don't want to keep replacing fuses. This is what I had in mind -

CTECHi Portable Power Station 300W, 299Wh LiFePO4 Power Station, Solar Powered Generator for Camping, Battery Backup Power Supply for Home Emergency Use, Outdoor, CPAP, Trip and Fishing https://a.co/d/3xXSUxb