For many years (maybe still?) Teslas did not have AM radio because the motor systems were too noisy and IIRC Mask claimed there was no way to solve it. I take this claim with a grain of salt. Lucid's have AM/FM HD radio. I don't have mine yet, but others can likely report if AM radio is usable.
I suspect if AM is useable, your radios should be OK as well. Also in addition to the police interest in Lucid, many police departments have Teslas in their fleets.
Funny EMI story: I worked at Ampex for a time around 1984. Ampex Digital Optics (ADO 1000) was the leading edge of video special effects. It treated live video as a plane in 3D space allowing it to be transformed. internally it used a 13.5Mhz clock. The single channel version had A/D conversion, digital manipulation, and D/A conversion all in one rack-mount unit that cost north of $100k in 1984 dollars. As far as EMI was concerned, the digital signal were well contained.
But they wanted to combine multiple channels into a single image with 3D interactions. This required cable connection of 13.5Mhz parallel digital data from the digital output stage to the Combiner box. They did their normal EMI testing and all was well.
Square waves, such as the digital clock signal, contain every odd harmonic n, at an amplitude of 1/n. Someone noticed that the 9th harmonic of 13.5Mhz is 121.5 Mhz--the VHF Emergency band. Interference in that band would be extremely bad, so they had to go through another round of testing just to confirm that band was not impacted (It wasn't, Ampex had some really good engineers).