I used two cameras+lenses:

Sony 𝜶6500 with Minolta 500/8 AF Reflex (EXIF reports 496 mm = 744) The lens is fixed length.
Sony RX10 IV with 220 mm lens (EXIF reports 220 mm=600). The zoom lens is not interchangeable.

Using a tripod, I shot the same target at the same distance with the RX10 at longest setting (Minolta is a prime). The picture, exposure, etc. are not important because the dimensions of the lenses, sensors and distance to target are the only things being compared.

744 / 600 = 1.24 so if the equivalent focal length were really only about the physical size of the sensor, the displayed image from the 𝜶6500 would be 1.24 times the size of the one from the RX10 IV.

Skip the math. The screenshot shown here tells me that in order to make the shot taken with the RX10 IV as large as the one taken with the 𝜶6500 + Minolta 500 it was necessary to increase the smaller image by 49%.

If we care about what the equivalent focal length means then either the 𝜶6500 is 894 or the RX10 is 499. Of course, the truth could be some mixture/hybrid of the two discrepancies.

It's a shame there is no standard to use for pixels per mm on the sensor so all we can do is compare lens and sensor combinations to each other. The discrepancy here appears to be the difference in pixels per mm in the horizontal dimension of the sensor.

The second screenshot that I added as an edit shows the RX10 shot with one using the 𝜶6500 with a Sony 70-400 on which the EXIF says 400=600. Same two cameras, supposed to be the same equivalent length. Twelve % difference.

This seems to be a very contentious topic. I wish camera makers could have thought of a better way to state the focal length for the various sensors. Someone will post something about the focal length he used, and someone else will say he's incorrect. It's the "equivalent" focal length. Does it really matter? No. You select your lens or your zoom length, and you take a picture.

A similar topic is "depth of field." That's been beaten to death, but it keeps coming back to life. Something is either in focus or it isn't.

"Standard" focal length on a 35mm was selected as 50mm. It makes something that is 20 feet away in real life look 20 feet away in the picture. Little or no subject magnification (positive or negative).
Less than 50mm pushes the subject back, greater than 50 brings it closer.
"Standard" for different <film/sensor> formats is different, that's why they use a conversion.
Base reference is the 35mm film format.

Thank you all for your (perhaps) accurate but trivial critiques of my simple demonstration. Let’s skip to the "thought experiment".

Let us use one lens. 100 mm prime, for example.
Let us use two cameras. For example, Sony A7Riv and A7iv

The A7Riv has a horizontal pixel count of 8448 pixels.
The a7iv has 7008.

They have the same aspect ratio.

They are both full frame sensors. The EXIF will report the same equivalent focal length for both. The angle of view is the same. The physical size of the image on the sensor is the same.

Take a picture with each of the same subject when focused at the same distance. Use infinity if you prefer. Use the same exposure and ISO.

View the pictures on the same monitor at the same screen resolution: use 100% for the A7Riv. You will need to use 8448/7008 = 120.5% to get the same on-screen image size for the A7iv.

If you want to print, then if you use the same relationship of pixels to dots for both prints the same ratio will apply.

Is it clear yet?

This seems to be a very contentious topic. I wish camera makers could have thought of a better way to state the focal length for the various sensors. Someone will post something about the focal length he used, and someone else will say he's incorrect. It's the "equivalent" focal length. Does it really matter? No. You select your lens or your zoom length, and you take a picture.

A similar topic is "depth of field." That's been beaten to death, but it keeps coming back to life. Something is either in focus or it isn't.