You could use something like this:-
https://www.ebay.co.uk/itm/USB-to-D...tep-Up-Cable-5-5-2-1mm-DC-1M-BSG/184294766936 to run the light strips at 12 V.
I would suggest you only run one, or at most two, from a power bank. The 12 V strips take 5 W, so at the 5 V output of the USB, that is 1 A. However the converter won't be 100 % efficient so it will be more than 1 A, maybe 1.2 A, so running two from a power bank pushing the limits.
I suggest you use several small power banks. Even the big power bank you liked to is only rated at 2.4 A (corrected from where I put the wrong units). Being larger makes it last longer, not produce a higher power.
Using a power bank like that isn't efficient, but it's an easy thing to put together. You could have a somewhat more efficient set up but it would need electronics to be designed and built, which would be a lot of work.
A power bank has a Li-Ion battery that runs at between 3.4 V and 4.2 V. The power bank has a boost circuit that increases that to 5 V for any battery voltage but that boost circuit has an efficiency of maybe 85%. The converter that I suggested has an efficiency of maybe 85% as well. The LED strips will probably have 3 LEDs in series, maybe 3.2 V each, so 9.6 V and there will be a resistor to limit the current that is also a loss of power, so the efficiency is 9.6/12 = 80%.
The overall efficiency is just under 60%, so less than 60% of the battery power will make it to the LEDs and the rest will be lost in heat in electronic components. If you had a current limiter and ran 3.2 V LEDs from the battery the efficiency would be between 76% with a full battery and 94% with a nearly empty battery. Alternatively you could have a converter to convert the battery voltage directly to the LED voltage, with suitable current control, and you might average 90% efficiency, but you would need to have batteries that are not in a power bank, and the loose LEDs.
So using a power bank, a 5 to 12 V converter and those LED strips means that your batteries need to be 1.5 times as big as with the best circuit. However for making one rig from off-the-shelf components, and having an easy way to charge the batteries, I would recommend accepting some slight limitations.
I agree that a lot of the stuff from Ebay will be poor quality. However most of it works, and with lighting you can see if the overall effect is what you want.