<< It is not semantics.

Oh, it is absolutely semantics. Allow me to elaborate.

<<there is no voting process, which is a necessary prerequisite for an “election”.

We might be approaching an interesting philosophical territory here. North Korea had elections[4]. There is a voting process. Kim Jong Un won 100% of the votes. Has an election, philosophically speaking, taken place? Is Kim the elected representative of the masses? Is the existence of a voting process truly a prerequisite for an election to take place?

To put it more subtly, who do you think voted in NK ( apart from the 100% that is )? Whose vote truly did put Kim in? Who was the true electorate? Now ask yourself the same question when it comes to HoL. Who has the power to make that decision ( to elect/to choose/to appoint/to crown -- whatever verb you want to throw in there )? Who has the power to actually vote here? Is it one person? Is it more than one? Do they have to agree? Using your framework, the power to influence this event is the actual election. The vote, as it were, if it truly is a prerequisite, happens behind the eyes.

<< It is not “elected by a very small group of people”

I would encourage you to visit some of the links in my previous post:

"Members of the House of Lords are appointed by the King on the advice of the prime minister."

Note that this is not me making this stuff up, it is British gov website saying just that[1]. Now, I understand that it is upsetting, because you are ( possibly I am only guessing for dramatic effect ) not the one doing the electing or voting, but understand that even that appointment is, in fact, an election. It would not happen if someone sufficiently powerful would consider it sufficiently beneficial to throw a wrench in the cog.

Now, do you know why it is rarely worth the effort? It is because HoL has now 758 members. You are saying some are hereditary and that is true, but even that number was lowered after 1999[3] to 92 ( how many would you wager are encouraged one way or another to participate or not participate for that matter? )

<<with terrible appointees frequently being rewarded for personally closeness

This is exactly my point! The election happens. You just personally do not like the factors that influence that election process.

<<there is no voting process, which is a necessary prerequisite for an “election”

I am simplifying, but when King says "It shall be so" on advice of the prime minister ( he effectively votes with PM's 'advice'; naturally, by advising, so does the PM ) that is the election. I think you are trying to attach structure that has been sold to most people as a voting process, but it is clearly at odds with simple political reality.

It might help if we look at the etymology of election and selection(appointment).

Elect:

Borrowed from Latin ēlēctus, past participle of ēligō (“to pick out, choose, elect”), from ē- (“out”) + legō (“to pick out, pick, gather, collect, etc.”);

Select:

Etymology. From Latin sēlēctus, perfect passive participle of sēligō (“choose out, select”), from sē- (“without; apart”) + legō (“gather, select”).

As you can see from the stem, they are effectively the same word. Now, a lot of people have been convinced they are different ( you mentioned votes as a differentiating factor ), but they are, in fact, the same process.

You could, naturally, to an extent, reasonably argue that selection is not the same as appointment, but if you you look at etymology of appointment you will see the following using your favorite search engine:

'The etymological sense is "to come to a point" (about some matter), therefore "agree, settle.'

Would you not agree that the agreement or settlement would automatically necessitate at least two parties to agree ( and therefore vote their opinions ) on a given decision?

Like I said. Semantics.

[1]www.lordsappointments.gov.uk
[2]https://lordsappointments.independent.gov.uk/
[3]https://en.wikipedia.org/wiki/House_of_Lords#Hereditary_peer...
[4]https://www.nbcnews.com/news/world/kim-jong-un-wins-100-vote...