I have not read the whole thing, so forgive me if I blunder.
Seems the circuit has seen much attention. Not my forte, so I won't go there.
Don't know much about your application area, but ...
If 40kHz has a period of 25 micro seconds, your 20 micro second pulses are each almost one cycle. The transducer resonance will help, but not have enough time to build up. The resulting pulse will get you a little bandwidth, if you are looking to use it.
20 micro seconds in water at about 1500 m per second is about 30 mm, or at least 15mm blind time if you are monostatic/colocated transmitter &receiver. One second return time gets you about 750 meters, if you don't have much reverberation. Any idea of the transducers' parameters?
If you have any sort of matched filtering in mind, longer pulses get you more energy in the water & hence more SNR out of the matched filter. If you don;t mind the longer blind time, while transmitting. Similarly, more frequent pulsing will get you more energy if you don't need the range & have a way to integrate it.
40kHz is quite low for underwater, will tend to get you range, but be bulky, especially if you want any directivity. Directivity will help with range/SNR. 40kHz is a traditional choice for air. You have some matched for water or a way to couple them?
Those filters you mentioned are usually to gain some SNR. No idea how your link budget looks, as in expected SNR. "The sonar equation" is not so fierce after you stare at it a bit.
Generally as soon as you sample, you alias all noise into the band you are using. If you're planning to use baseband sampling, that is, sample at least twice the highest frequency expected, you'll bring all noise present into this band. So digital filtering will narrow that a bit, but you can't exclude any higher frequency noise, as it is now in-band. If you run the sampler faster, you can then reduce bandwidth digitally, but your gains are limited unless you oversample by quite a lot, eg 3dB per doubling/halving.Multi-rate filtering/decimation can reduce your computational load for the filtering. For many serious applications you just can't do it without some filtering prior to sampling.Badpass may be needed. You could look at bandpass sampling if you're that way inclined.
There have been some dead simple sonar circuits that use an RF receiver chip for the receiver. The RSSI is your output signal, being nicely log already. These are cheap & can be worth looking at.
Sorry, too long ago for me to remember numbers.
If those cleaning transducers are omnidirectional, a lot of your power goes into spherical spreading.