The stator of the thruster is sealed. The green covering of the coils.
But the ESC you linked to is not sealed. This means you have to make connections
from the battery and the ESC to the motorcabe inside a housing and then the cable that goes outside to the outside mounted thruster has to be sealed.
If the housing is carefully sealed against water, inside the housing you can use normal components and normal contacts.
So any kind of 3S-Lipo manufactured for the use in RC-cars or RC-planes will do.
Motors for RC-cars and RC-planes easily draw 20, 30, 40 , 50 amperes and need a high amperage battery.
The discharge-current of these Lipos is specified as "X"C where the number for "X" is the factor you multiply the nominal capacity of the battery
Example:
A lipo 3S 2000 mAh rated 20C means:
the maximum discharge-current is
20 x 2 A = 40 A (20C meaning twenty times the capacity)
Almost any RC-car / RC-plane Lipo will have minimum 20C.
Most of them will have 30C or 40C and you can buy Lipos that go up to 70C
3S means 3 3.7V-cells are connected in serial which means 3.7V + 3.7V + 3.7V = 11.1 V as nominmal voltage.
A Fully charged Lipo-cell goes up to 4.2V so 3S = 3 * 4.2V = 12.6V
Attention ! For charging LiPo-batteries you need a special suited LiPo-charger.
If you ever load a LiPo to more than 4.2V per cell the LiPo-battery will catch fire!
The voltage of each cell has to be monitored to not exceed 4.2V. This is the reason why such LiPos have so called balancer-plug. With this balancer-plug the voltages of each cell will be monitored.
If you do pretests of the thrusters with longer wires and the battery above water
a 12V lead-acid-battery that is able to dis-charge with a current of 30A will be sufficient.
You should not reach the maximum dis-charge-current of the battery.
A battery with max dis-charge-current 25A is too close to the limit with 2x 11.5 = 23A
So my recommendation is a 12V lead-acid-battery dis-charge-current minimum 30A
Any even used 12V car-battery with a capacity of 40 Ah will do.
(though these car-batteries need 12 hours to re-charge.
Or a LiPo of minimum 30A / 20C = 1.5Ah = 1500 mA.
If a 20 Wh battery is empty after 5 minutes highly depends on if you were running the motors on full throttle continiously or not.
For your pre-tests another option would be to use a high amperage power-supply 12V 30A
Or using a Lipo 3S 3000 mAh which would have
3 * 3.7V * 3 Ah * 80% = 26.64 Wh
Something like this
https://hobbyking.com/de_de/turnigy-battery-3000mah-3s-20c-lipo-pack-xt-60.html
Such batteries can be charged in one hour
plus a LiPo-charger
https://hobbyking.com/de_de/turnigy-accucell-6-80w-10a-1-6s-balancer-charger-suitable-for-lihv.html
No idea where you are located. If your town has an RC-model shop you could look there for a special offer
best regards Stefan