My question is not about the implementation of those waits. It’s entirely about the statements and calculation of timeout on the doc.
But you have to know how they are implemented to make sense of what is going on. Here is what happens with your mix of the two types of waits. I’m kipping over those steps that are not important for the discussion.
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Your script sets an implicit wait.
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Your script starts an explicit wait checking whether the element exists. The explicit wait works by polling. So it sends a command to the browser to check for the existence of the element.
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Because of the implicit wait already set, the command sent to the browser takes 10 seconds to return a failure.
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Your explicit wait checks whether it has reached its time limit which is 15s. It is currently at 10s (+ a tiny amount of time taken to execute the script, network latency, etc.) into the wait, which is less then 15s. So it is not done waiting and reissues the same command as in step 2 above.
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Because of the implicit wait, the command sent to the browser takes 10 seconds to return a failure.
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When the explicit wait checks again for its own timeout, more than 15s have elapsed, so it times out.
So the explicit wait polls twice, and each time takes 10 seconds which mean 20 seconds total (plus a tiny amount of time to account for the bookkeeping).
An explicit wait does not do anything to detect and compensate for an implicit wait that has been set. And it does not continue running in parallel to the commands it sends to the browser. While a browser command executes, the explicit wait is not doing any bookkeeping or able to time out. It has to wait for the browser command to complete before checking whether it should time out.