Electronic – Length of the dipole antenna

Unfortunately, there are some problems with your ask.

First, that video doesn't detail the construction of a half-wave dipole, but a monopole with a 1/4 wave sleeve around the coax feed to decouple the line. Mounting them can be problematic since none of the conducting surfaces are at ground potential. In other words, you can't just bolt the bottom section to a mast with metal fasteners.

Just because you solder the other half to a piece of metal doesn't make it an effective second arm of the antenna (e.g. dipole). It's (1) aligned with the feed line and (2) completely surrounds it at equal potential. This won't radiate in the far-field. What this structure actually does is load the feed point of the antenna allowing it to look electrically longer or shorter than it physically is (see "antenna tuning" or "antenna matching") and presents a virtual ground impedance very close to the feed point making the precise location/orientation of a real solid ground plane less critical.

Submerged Antennas...

Second, transmission in fresh water doesn't work the way you've described because the water polarizes and therefore the attenuation factors are extremely high and your dielectric coefficient goes way off. Most transmissions of "underwater" antennas don't actually propagate through the water, but above the water (or at the air-water interface) by radiating off of the return path (outer conductor) of the cable... and this is a low-efficiency transmission obviously.

Or... because the air pathway is so much less attenuating, any energy is more likely to go "up-over-and-down" (or "down-over-and-up") rather than directly, even at short distances.

Here's a figure from my book that illustrates this with the relative attenuation factors:

The height of a line (thickness of dielectric) affects both its capacitance and inductance. The width of a line affects both its capacitance and inductance. The length of a line affects only its delay, and its attenuation.

If a transmitter and an antenna are the same impedance, and connected by a line of that impedance, then the length of the line connecting them is irrelevant (except for ohmic losses causing attenuation).

However, often the transmitter isn't matched for some reason, power or efficiency, and the antenna may not be matched, perhaps for space, and the line between them is used for matching. In that case, the maximum matching effect can be achieved with a \$\lambda/4\$ or odd multiples of that length line. With a \$\lambda/2\$ line or multiples, no matching impedance transformation is achieved, regardless of the line impedance.