"Pro-Kremlin" is the wrong way of categorizing it. BILD is right-wing and populistic first, low standards and always loving to rile up people second (or as a popular German song once said it: BILD only ever produced "fear, hatred, tits and weather reports"... and the latter two are nowadays sadly missing). And their most important purpose right now is attacking the German government to get their beloved conservatives back. (PS: Oh, and BILD's ex-editor in chief is nowadays leading the creation of a mostly internet and social media based fake news network (fittingly for such a shitshow named NIUS - as misspelling things is probably their least serious flaw)).

It's entirely irrelvant if what they say is matching Kremlin propaganda right now or telling the story of how German government idiots are blindly supporting the US to our own detriment or stupidly trying to build renewables while destroying the whole country with that nonesense. If it's reflecting badly (for some of their readers) on the German government, then it's a story BILD will push. Military support for Ukraine is widely supported by the population, so telling the story of how the government is secretly trying to undermine Ukraine supports fits their agenda.

As an example of how they then even manipulate news:

Do you remember the discussion about Lithuania blocking rail transports to Kaliningrad last year? While that discussion happened several politicians were asked about their stance on a EU summit back then. They basically all answered the same: That this needs to be analysed based on international rules and also in regards to the fact that it's about transit between two Russian territories. And that this is a EU discussion, not something Lithuania should decide alone.

That was very obviously an EU line everyone was just repeating. Yet BILD first reported on it, citing the German chancellor and the Polish PM (amopng others) first with full context, then repeated it with only Olaf Scholz as the sole source and less context on POLITICO (also belonging to the same German publisher as BILD) (Title: "Germany’s Scholz urges free transit for Russian goods to Kaliningrad - German chancellor said that ‘we are dealing here with traffic between two parts of Russia,’ suggesting that EU sanctions should not apply") and then within less than 12 hours they reduced the original article to about 15% of its original content (and by that time several international news linked to that report as their source)... now also with Scholz as the sole opposition to the Lithuania's ban and with all context removed so their own invention that "EU sanctions should not apply" was now magically a fact.

And that fake story of how "Germany is trying to support Russia and to undermine sanctions" was then the discussion internationally for days.

Or as another shorter example: Has anybody ever found those 100+ Marder IFVs in ready-to-deliver condition that Rheinmetall was trying to deliver in April 2022? Blocked by the evil German government via lies about their existance... That was also a BILD story. Soldiers in the Bundeswehr are probably still questioning why they had to find spares to actually deliver vehicles to Ukraine nearly a year later and workers at Rheinmetall wonder why they have to refurbish old stocks for 1 1/2 years now, when there is a magical batch of vehicles somewhere bigger than everything they produced in that year.

EDIT:

And here we go: That other piece of waste paper picked up the story, also adding more fairy tale details of how Olaf Scholz is fighting the Minister of Defense he actually appointed on Ukraine support as "It becomes ever more clear that the chancellor does not believe in a Ukrainian victory and does not want one at all!"... Let's see how long it takes for US sensationalists to pick it up now (the title at least refers to US and Germany, even if they then totally forget that the US exists...), get it debunked by the US government to leave us with another week of "why is the German government so stupid and still supporting Russia?"

With a bit of luck you can even see the BILD source adapt in real time this time as the fairy tale is spun further and fleshed out...