JBL Tour Pro 3

Yes, the headphones have Multipoint Connection, which allows you to switch seamlessly between the connected devices. 

It is not uncommon to have charging problems with True Wireless headphones. You may encounter that charging stops, does not start at all or that one of the ear buds suddenly switches on and begins the pairing process. This is almost always caused by dirt on the metal charging contacts. These contacts are vulnerable because they can easily be contaminated by sweat, skin grease, or ear wax. They are usually gold plated, but gold plating does not prevent surface dirt.

If you have charging problems, the first step is to always clean all contact points, on each earbud and on the charging case.
You will need: cotton cloth or makeup swab, cotton swabs and rubbing alcohol. Also a pencil with eraser for further cleaning.

Use a cotton swab with some rubbing alcohol to clean the charging terminals of the headphones. Rotate the swab and scrub lightly on each contact surface, then use a cotton cloth to remove any dust and cotton residue left on the headphones. It is important to perform this process periodically to keep your headphones clean, thus avoiding affecting the charging speed/quality.

Wipe the contact pins in the charging case with a clean cotton swab. The swab can be slightly moistened with rubbing alcohol, but it is important that the interior is completely dry before closing the box. Use the cotton cloth and wait for it to dry.

Repeat until the contact points are visibly clean, and charging should work as designed.

Try cleaning the contacts with the tip of a pencil and the eraser at the end of the pencil, the graphite and rubber can help to re-establish charging also.
This procedure can be performed on all True Wireless Stereo earphones and cases.

The JBL product is in a deep sleep mode, which it is to prolong the lifetime of the battery. Connect the case to a charger for about 2 seconds to wake the product up and take the earbuds out from the case. Once you put the earbuds back in the case, it's ready to pair through Bluetooth. 

Double-tap the button on the right earbud, then on the third tap - press and hold the button for more than 5 seconds (until the unit shuts off). 
This restores the earbuds to the factory defaults.
TWS must be connected to perform the reset, so neither of the earbuds should be off or in the charging case.
It also may be necessary to remove or forget the earbuds from the list of paired Bluetooth devices in order to pair again.

Personi-Fi 2.0 is a new feature available through the JBL Headphones App. This feature helps to personalize the sound using the best possible sound curve based on your hearing capabilities. It will first ask a few questions, and then check your current ambient audio. You will be informed that this step should be completed in a quiet environment. It will play a series of test tones in all the different frequencies wherein after each frequency test tone is played, it will ask you what is the lowest volume setting you can hear. Nine different sounds will be played in each ear (18 in total).

Simply press and release the button when you hear a sound. After it goes through all the test tones, it then calculates the best sound for your ears based on the results. It allows you to demo the results by playing a track. You will be able to toggle it on/off to hear the difference.

This headphone is supported by the My JBL Headphones App.