I did a few experiments with Pro-Q3 (FabFilter) to see if I could identify the clicks; but after a while I realized the clicks occur at several frequencies rather than at a handful of frequencies, where perhaps an ideal scenario is where the clicks are at 60-Hz, which would be typical for fluorescent light or something interfering from nearby electric power (for example 120V at 60-Hz, which in the US is what it's supposed to be but is not so precise all the time, hence having a line conditioner can be helpful).
The next thing I tried was Google AI; and it suggested a few VST effects plug-ins that claim to remove clicks.
One is "X-Click" (Waves), and the other is iZotope RX, which has a de-clicker module.
(1) Pro-Q3 (FabFilter) is good when clicks are consistent, but I was not able to get good results with it.
(2) X-Click (Waves) is good for showing the clicks but did not do a very good job removing the clicks.
(3) RX De-click v10 (iZotope) worked the best, and with more steps and additional techniques it might be part of a good solution.
The YouTube video shows RX De-click v10 removing clicks in a fixed setting on one-pass. A section of the YouTube video plays the clicks, which is an option, but then it goes back to playing the de-clicked audio.
THOUGHTS
Everything is important; but one way to explain the way this stuff works is to consider that it's recording made by Elvis Presley or John Lennon on a home recording device that has a lot of clicks, wow, flutter, and other annoyances. Whether a VST effects plug-in can correct all that stuff is another matter; and it might be necessary for a software engineer or audio-engineer to examine each microsecond to remove clicks, which might be cost effective and probably was the way Beatles were able to create the last song with John Lennon, which includes one of George Harrison's last performances. It used a home recording John Lennon made on a cassette player; and although I have no inside information, I am confident suggesting that a team of audio experts worked on John Lennon's singing on the cassette tape.
IDEA
If I were working on this choral performance, intuition suggests adding strings to mask the clicks that remain after iZotope RX De-click v10 does it's work, which from a practical perspective is an
arranging activity and is what George Martin did when he arranged and composed the double-string quartet for "Eleanor Rigby" (Beatles), which is Paul McCartney's singing plus the strings,
ANALYSIS
Adding to the suggestions and ideas from everyone else and using some of the information I discovered in my de-clicking experiments, I do not think the clicks are all from fluorescent lights, electric motors, or things like that, because the clicks are more random than steady, where for example even if it was caused by a variable speed electric motor, one would expect the clicks to track the speed of the electric motor in a way similar to a series of glissandi and similar to the way a engine sounds when it' revved.
The organ is a bit loud and the choir is not sufficiently loud; and this suggests an improvement in the future will be to focus more on where the microphones are placed relative to the choir, as well as the levels of the microphones recording the choir.
If the microphones are wireless, BlueTooth, or not XLR microphones, then that can be a source of the problems.
Anything is possible, and there are high-quality wireless microphones that singers use in concerts; but that's another matter.
If possible, I would use XLR condenser microphones run with XLR audio cables to an external digital and MIDI interface like a MOTU 828m3 Hybrid, which then would be connected to the computer, thereby ensuring there will be no interference clicks from whatever the audience and everything else is doing (fluorescent lights, electric motors, cellphones, and no telling what else).
If the organ really was loud, then I would ask the organist to lower the volume so people can hear the choir; but depending on where the microphones were placed, the organ volume might be good, which makes it more of a matter of where the microphones are placed relative to the choir.
This is what comes to mind at the moment.