There are two issues here. One is the definition of the term "elected" and the second is whether a councillor is elected when technically there is no poll.
The amendment in 2022 was to incorporate otherwise outstanding amendments in previous legislation so it didn't introduce anything new; just confirmed amendments previously included in other legislation. Without spending a lot of time looking for it, I can't quote the actual legal reference for co-opted councillors being classed as "elected" but the 1972 Act did provide the power for local councils to co-opt members where there were insufficient candidates at an election and/or where a casual vacancy occurs and there is no demand for an election by the electorate.
My understanding of the requirement for there being a minimum of 5 seats on a parish council is a reference to there being a need for at least five seats in any parish council, regardless of size of the electorate. A quorum is defined as one third of the number of seats (rounded up where this is a fraction) or a minimum of 3, whichever is the larger figure.
Elections are held every four years (also by virtue of the 1972 Act) but where there are the same number of candidates (or less) than there are seats the Act also provides for those candidates to be automatically elected. There does not have to be an actual vote to have taken place. Remaining vacancies can be filled by co-option as soon as practicable after the date of the election. Where there are less candidates than the minimum number required to form a quorum, the principal authority can fill those vacancies in the short term to enable a council to act to fill those vacancies by co-option.
It is not uncommon for the electorate to believe no elections have taken place when there is no poll. Despite notices everywhere (notice boards, websites etc.) and a huge amount of publicity, the whole local council election process does seem to pass many people by. This is unfortunate but does not render the process unlawful.