Relative pronouns "which" and "that" vs. "welches" and "das"

Question

(Related: are "das", "was" and "welch-" interchangeable relative pronouns?) In English the "rule" is that "that" is used in restrictive clauses while "which" is used in non-restrictive clauses. (See the usage note here). For example:

The event featured musical numbers performed by many artists. The song that Ella Fitzgerald sang was written by Cole Porter.

In this case, there were many songs, but only one was sung by Ella, and the clause restricts the sentence to that song. In contrast:

The event included many performances including a musical number. Ella Fitzgerald sang the song, which was written by Cole Porter.

In this case there is only one song and the clause is simply adding an additional fact about it.

I put "rule" in quotation marks above since few native English speakers are aware of it or follow it scrupulously. To my ears

The song which Ella Fitzgerald sang was written by Cole Porter.

sounds fine and has the same meaning. But

Ella Fitzgerald sang the song, that was written by Cole Porter.

sounds odd and I'd probably assume that I'd misunderstood something. So, at least in my Inland Northern American variety of English, the rule seems to be that "which" and "that" are interchangeable in restrictive clauses, but only "which" can be used in non-restrictive clauses.

Translating to German, DeepL seems to think both das and welches work in both sentences:

Das Lied, das/welches Ella Fitzgerald sang, wurde von Cole Porter geschrieben.
Ella Fitzgerald sang das Lied, das/welches von Cole Porter geschrieben wurde.

Wiktionary says that welches would not be used in spoken German, and even in written German it would be seen as overly literary and pretentious. This would mean that welches is, at least in modern, idiomatic German, not used as a relative pronoun at all and you'd always use das regardless of whether it's a restrictive clause or not.

DWDS says that welches would be used either when the word immediately following it is similar, in other words a definite article, or when there are several clauses in succession. Their examples:

das Kind, welches das schönste Bild gemalt hatte (I can understand why das das would sound odd.)
das Geschäft, das mir das Gerät verkaufte, welches mir so viel Ärger bereitete, will es nun doch zurücknehmen (The device, not the business, caused the trouble.)

So does the restrictive/non-restrictive issue make any difference in German? Is welch- used as a relative pronoun in today's German? I've learned to trust neither DeepL or Wiktionary completely. I trust DWDS more but I understand their mission is to define words and not necessarily to delve into issues of usage and grammar. I am convinced though that, whatever may be the case, English and German do not agree on this. English speakers don't seem to agree even among themselves.

Answer 1

• "So does the restrictive/non-restrictive issue make any difference in German?"
  No, it doesn't make any difference in German. I also never heard about this difference in English. But English is a foreign language to me.

• "Is welch- used as a relative pronoun in today's German?"
  Yes, it is used, but only as the unpopular second choice. "welcher/welche/welches" is the out-of-favor alternative for "das" that only is used when the usage of "das" would give two copies of "das" next to each other. But even in this situation most people prefer double-das:

  1. Wir reden heute über das Kind, das das Bild gemalt hat.
  2. Wir reden heute über das Kind, welches das Bild gemalt hat.

  Both sentences are correct. In spoken German most people would use version 1, in written German you will find more often version 2. The same is true for this pair of sentences:

  1. Ich sehe das Geschäft, das mir das Gerät verkaufte, das mir so viel Ärger bereitete.
  2. Ich sehe das Geschäft, das mir das Gerät verkaufte, welches mir so viel Ärger bereitete.

• "I've learned to trust neither DeepL or Wiktionary completely."
  It's a good strategy to doubt artificial intelligences (DeepL) or groups of amateurs (Wiktionary), but that doesn't mean they're always wrong. In more than 95% of all cases, they are right. Btw: Now you trust German.stackexchange which is a group of amateurs.

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Native speakers who already are familiar with the usage of welches often use this word to decide if "das" or "dass" is the right choice after a comma. The replacement of "das(s)" by "welches" only works if the word in question is a relative pronoun, and only "das" can be a pronoun while "dass" is a subordinating conjunction.

Auf dem Tisch steht das Glas, das/dass du mir geschenkt hast.
Auf dem Tisch steht das Glas, welches du mir geschenkt hast. - correct, therefor:
Auf dem Tisch steht das Glas, das du mir geschenkt hast.

Bist du sicher, das/dass das dasselbe Glas ist?
Bist du sicher, welches das dasselbe Glas ist? - wrong! therefore:
Bist du sicher, dass das dasselbe Glas ist?

Bzw: Native speakers have no qualms about producing sentences like this:

Der Philosoph behauptet, dass das das Dasein verändern würde.
^{The philosopher claims that this would change existence.}