You can also use one of those power banks for cell phones. They come in various capacities and provide regulated output voltage.
In general, power banks that support 6 volts directly are fairly rare. The majority of power banks just support 5 volt USB power.
The new standard is USB C PD (power delivery), which can provide USB 5 volt power, but a device can request that it get a specific voltage and a specific max amps. IIRC, 5, 9, 12, 15, and 20 volts are typical voltages that you can get from USB C PD, but I don't know if the newest version of PD allows for other voltages. You can get so called trigger cables that fix the voltage at 9, 12, 15, or 20 volts.
One problem with power banks is often times they are designed for cell phones, and if your project does not pull enough power, it will shut down.
My favorite power banks that include USB C PD and also have US style plugs for recharging are, which I use for powering digital cameras as well as charging cell phones:
The older standard is QC (quick charge) that cell phones can request higher voltages and amps. I am not aware of ways to plug into a USB C QC power source to get a specific voltage.
There are a few power banks that provide specific voltages in addition to USB (typically 9 volts and 12 volts). The only one that I'm aware of that produces 6 volts is the AILI power bank (sold by a few different sellers), which needs 6 18650 batteries (you would need to buy the 18650 batteries separately):
In the past, there was a power bank where you could dial in the voltage, but it does not appear to be made any more.
One way to get specific voltages is to use step-up or boost (convert a smaller voltage to higher voltage), step-down (convert a higher voltage to lower voltage), or step-up/step-down (convert high/low voltage to a specific voltage). Note, there are various trade-offs involved such as max power the regulator can draw, max power that your battery provides, the amount of heat generated, and how much power is lost during conversion. I tend to go to pololu.com to get them:
So you might want to consider 2 voltage regulators, one for producing the power for the Teensy (3.7 - 5.5 volts), and the other for your motor. You would plug these into the same power source. Or get one regulator for the motor and get a power supply that provides 2 separate power ports including a USB port for the Teensy.
If you go to shops that support radio controlled cars, etc. they often times have batteries with different voltages. For camera stuff, I've been playing with battery holders for Sony NP-F batteries used for video. The camera batteries tend to have 2 li-on cells, so they produce voltages between 8.4 volts (when freshly charged) and 7.0 volts (when nearly depleted).
In terms of AA batteries, they also can vary in terms of voltage produced. Non-rechargeable batteries start out at 1.5 volts, but after use, they quickly put out a lower charge. So if you have a 4 battery holder, it will initially produce 6 volts, but it will drop over time. Rechargeable batteries produce voltages around 1.2 volts (so a 4 battery holder would produce 4.8 volts), but again the voltage varies over time.