molecular biology - What makes/breaks the hydrogen bonds between DNA and RNA during transcription?

So I know that RNA polymerase catalyzes the phosphodiester bonds that hold the sugar backbones of a growing mRNA molecule together during transcription. However, I'm less sure about the hydrogen bonds between the nitrogenous bases of the forming RNA and the template DNA strands.

I do assume that hydrogen bonds are forming, but they must be short-lived. Their existence are confirmed here:

ribonucleotides containing 3 phosphate groups hydrogen bond through the process of complementary base pairing with the exposed deoxyribonucleotides on the unwound strand that is to be transcribed

and represented in this gif:

Is RNA polymerase responsible for creating the hydrogen bonds between DNA and RNA? Is it, then -- I assume -- also responsible for breaking these bonds? Are the breaking bonds driven by chemical reactions or more due to the physical movement of the polymerase along the DNA template?

This site mentions the transient H-bonds formed by holoenzyme at promoter sites, but I haven't been ale to fnd a reputable source discussing the transient H-bonds between nucleic acid strands.

I'd appreciate if someone can provide a clearer molecular description of what's going on here. Pictures/animations are a plus!