The telescopic won't be much better. A dipole is optimum for indoor use:

https://www.amazon.com/Parts-Express-FM-Dipole-Antenna/dp/B000M9EREE/ref=sr_1_4?crid=32HFREASV10KJ&keywords=fm+dipole&qid=1660319983&sprefix=fm+dipole%2Caps%2C120&sr=8-4

If you already are using one of these and it's not optimal, then either an attic antenna or roof mount:

https://www.amazon.com/Stellar-Labs-30-2435-Outdoor-OMNIDIRECTIONAL/dp/B00DHHOZBI/ref=sr_1_3?crid=268E9Y1MX7LE6&keywords=outdoor+fm+antenna&qid=1660320055&sprefix=outdoor+fm+antenna%2Caps%2C113&sr=8-3

| "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