Soundcore Motion Boom Plus has an AUX in. It does turn off either after 5, 10, 15 or 20 minutes if nothing is being played. However while it's charging it goes into standby mode and will not power off.

You're better off getting the Motion Boom Plus for about the same price. The problem with the Sony's I can't find anything about then regarding the pairing. If you plan on putting them in different rooms you don't want them to be TWS ( True Wireless Stereo). You want your speakers to be in a sort of "Party mode" where each speaker plays exactly the same and not one being a left channel and the other the right channel. With the Soundcore you can actually do both. Either pair them as a stereo pair, or connect up to 100 speakers playing in sync.

Just my thoughts.