Naval architect here. As other commenters have noted the size of the pumps isn’t really the issue here - you can have as many as you want it really depends on the time you have available.

For me, the cool things about this are the size of the installed power and the stability problem in having one submerged object with multiple half empty ballast tanks lift up another object with multiple tanks.

The BOKA Vanguard has an installed power of 27000kW, split between two main diesels and two auxiliaries. This is slightly more than a Los Angeles class nuclear submarine, which goes much faster (perhaps 2x according to wiki) underwater - very much a different resistance problem. There are two 35 tonne and 65 tonne generators/engines. These are not small pieces of equipment. That’s what gets me about these ships - they are on another level of huge.

The stability problem is a significant challenge. You can see in the video that they did it on a flat day. Being able to coordinate the pumping of multiple ballast tanks to make sure that both ships remain upright is another cool thing here. Look up the “free surface effect” if you want to learn about that particular challenge.

Sources; various Wikipedia pages and Wärtsilä technical sheets.