The cable does not care or have 'compatible' questions, its only the connector that matters.
The TV coax will have an F connector, so you just need to adapt it.... Since you are going to run an LNA (yes, you are _going_ to run one, no question), then really its a matter of going from your SO239 to the LNA and from the LNA to the TV coax.
Here is the LNA:
https://www.amazon.com/Nooelec-SAWbird-NOAA-Ultra-Low-Applications/dp/B07TWPR871/

Then from the SO239 female (Assuming your antenna has a male plug - you never mentioned) you will need this:
https://www.amazon.com/DHT-Electronics-coaxial-adapter-female/dp/B00CVQOOAI/

Then from the LNA to the TV coax:
https://www.amazon.com/DHT-Electronics-coaxial-adapter-female/dp/B00CVTRTUC/

| "slip-on coaxial connector" ... Does anyone know what these connectors are, exactly?

It is a non-threaded female type-f connector, popular with home appliances because you don't have to screw it onto the threaded male connector. Just slide it on and off.

What you need is Type-F to SMA adapter, which screws onto your RTL. Then just slide the antenna F-connector on and off as needed.

https://www.amazon.com/DHT-Electronics-coaxial-adapter-female/dp/B00CVTRTUC/ref=pd_lpo_3?pd_rd_w=CLZd9&content-id=amzn1.sym.116f529c-aa4d-4763-b2b6-4d614ec7dc00&pf_rd_p=116f529c-aa4d-4763-b2b6-4d614ec7dc00&pf_rd_r=SQPQ0GN4BN5ZTY3H445K&pd_rd_wg=f7dHy&pd_rd_r=de1c4cbe-dfeb-49c5-b170-24284dfd1db9&pd_rd_i=B00CVTRTUC&psc=1

Looking at the reviews for the Terk, I tend to agree that this antenna will not perform to your expectation. An external antenna, even installed on a patio rail, will perform on FM much better. Maybe a DIY wire antenna or a (cheaper) commercial folded dipole like below. (A wire antenna would be best for general RTLSDR listening.

https://www.amazon.com/dp/B00DHHOZBI?linkCode=sl1&tag=radiopicker0b-20&linkId=7f420d1b1d32dba1bf60f1c8e341b0fc&language=en_US&ref_=as_li_ss_tl