Term that describes the technique in which an artist repeat lyrics from their previous work

Depending on the context or connotation you have in mind, I would say that the artist is either

• borrowing material from earlier work (or even work from other artists), assuming the connotation is that the common material was not intended to be an overt reference

or

• referencing earlier work, if the connotation was that this act was intentional

One could also talk about the intentional use of common themes throughout the artist's works, or state that their work is thematically linked, in which case you would just state that they're returning to that theme or you could talk about theme re-use.

I don't know a musical term but I've got a close one. See rehash, defined by Oxford dictionary as:

A reuse of old ideas or material without significant change or improvement.

Also look up basic words such as rewording.

To be honest, the phrases "Will you still love me...", "Heaven is ...", and "... the moment ..." are so common in spoken English that there is no rehashing of old lyrics going on with these artists.

For musical echoes of these phrases, look here:

The Shirelles had a big hit in 1960 "Will You Still Love Me Tomorrow." written by Carole King.

"Heaven Is" is a song released in 1993 by Def Leppard.

Then there's Tame Impala - "The Moment"