You may need a DOCSIS 3.1 compatible modem to reach advertised speeds.
Yes, you should get a new modem. Make sure it is DOCSIS 3.1 compatible. The SB8200 would be a good choice.
The speed displayed in windows is the ethernet/raw wifi speed. To see the speed, you nees to open th emanagment page of your router. To do that you need the local ip address(google is your friend) replace the last number of the 4 with 1 and enter that in your browser of the pc.
Spectrum upgraded my connection recently to 100/10 (Louisville, KY area). I had an SB6183 and the download speed was around 65 Mb/s. They sent me a new modem and the speed went to right at 100 Mb/s.
If a SB6183 couldn't do 100 Mb/s, I think there's no way a SB6141 could do 300 Mb/s, so yeah, I'd get Spectrum to send you a new one. They mailed mine at no cost and I self-installed it (without going through their stupid phone app; I had to call them instead).