For example, does an air traffic controller say the full phrase ("expected approach time XX minutes") or are there other conventions?
In the U.S., ATC would likely use the phraseology "Expect Further Clearance (time)" as opposed to "Expect Approach Clearance" or "Expected Approach Time..." as you say in your question.
The FAA's Order JO 7110.65Z (Air Traffic Control Handbook) does not use the phraseology "Expect Approach Clearance." Instead the phraseology used is "Expect Further Clearance." (see excerpt image from the 7110.65 below)
NOTE: The primary purpose for ATC using "Expect" phraseology is to provide for (IFR) procedural guidance regarding pilot actions expected in the event of loss of communication as specified in 14CFR 91.185.
This phraseology aligns with 14CFR Part 91.185 IFR operations: Two-way radio communications failure., (3) Leave Clearance Limit (i) and (ii).
(3) Leave clearance limit.
(i) When the clearance limit is a fix from which an approach begins, commence descent or descent and approach as close as possible to the expect-further-clearance time if one has been received, or if one has not been received, as close as possible to the estimated time of arrival as calculated from the filed or amended (with ATC) estimated time en route.
(ii) If the clearance limit is not a fix from which an approach begins, leave the clearance limit at the expect-further-clearance time if one has been received, or if none has been received, upon arrival over the clearance limit, and proceed to a fix from which an approach begins and commence descent or descent and approach as close as possible to the estimated time of arrival as calculated from the filed or amended (with ATC) estimated time en route.
(emphasis is mine)
One of our controllers may give a better answer, but if an aircraft was expecting to commence an approach on arrival but is instead given holding instructions by ATC, an expected approach time, or expected further clearance time should be given in the event of lost communications.
Typically phraseology would include the holding instructions, with the approach time given in minutes past the hour. For example: "N123Z, hold at ZIPPO as published, expected approach time four zero."
An expected approach time shall be transmitted to the pilot in case holding/delay in excess of 10 minutes is expected. Phraseology:
a) No delay expected
b) Expected approach time (time)
c) Revised expected approach time (time)
d) Delay not determined (reasons)
So in your example, the praseology would be along the lines of "Expected approach time 10:42"