I agree PHM was great (and I loved the book before the movie). But as a VFX person, please be careful not to buy into the currently popular studio PR line: "it's all real, almost no CGI". Media and influencers love this line and often unknowingly muddle the studio's very carefully crafted press release wording into outright lies by paraphrasing and making assumptions. The problem is these aren't just white lies, they deprive some very talented VFX artists from getting credit for amazing work.
About the misunderstood puppet: A real Rocky puppet was indeed used on set (actually a few different puppets) and some of the puppet is sometimes seen on camera. But most of the puppet was digitally replaced with CGI or CGI-enhanced in most of the scenes. However, using a much more realistic puppet on set is indeed notable but not because the character wasn't CGI. The puppet is worth talking about because it directly enabled the final mostly-CGI character be really good CGI. It's good because shooting the physical puppet gave the VFX character animators an ideal reference that's "grounded" in the physical reality of the set, camera and lens. The subtle interplay of light, shadow, texture and specularity in the CGI are all grounded in reality. The puppet also let the actor interact with something closer to reality. It's a wonderful technique and should be celebrated instead of obfuscated to promote a "No CGI!" falsehood that trends well on social media.
Also, PHM did use real sets (like most movies) and they were able to avoid using green screen for some of the ship exteriors but those backgrounds were still digitally replaced with CGI rendered elements, they just didn't use green screen to pull the matte. But on social media, "No green screen" (true) was conflated into "No CGI" (false). Instead of green screen they used a black backdrop with careful lighting and some hand rotoscoping to extract the digital mattes. Doing it this way had the advantage of not needing to digitally remove green spill on reflective surfaces by hand and it saved money over doing a StageCraft virtual volume at that size. Done well, a green screen could have produced the exact same shot but it would have cost more and taken longer.
But influencers and media are unintentionally perpetuating "No CGI" myths instead of focusing on the actually interesting, more nuanced reality. Using more and better physically grounded references on-set IS a breakthrough that helps turn bad CGI into great CGI. Another example is Top Gun where "artfully misleading but technically true wording" in studio press releases grew into outright falsehoods online. Tom Cruise was truthful in saying that he was flown in a jet right alongside other REAL jets doing simulated dog-fighting. The lost nuance is that all the other jets Cruise flew with in those dog fight scenes were old Soviet trainer jets that look quite different and are much smaller than real MIGs. So the trainer jets were entirely replaced by CGI MIGs in post and are never seen in the final film. And we couldn't tell because the digitally removed jets provided ideal grounded reference for the CGI pixels that replaced them. And that's how we ended up with several famous YouTubers proclaiming "These are REAL jets, not CGI!" while showing 100% CGI jets. Same with Wicked and the CGI tulips. The fact that Wicked used thousands of specially grown tulips on-set (true) was confused into proclaiming "ALL these tulips are real, no CGI!" (false) while showing a scene where >90% of the tulips were CGI.