Not fully scientific, but the newer seasons Sesame Street have adopted a catchphrase that is just a condensed version of the scientific method. "I wonder. What if? Let's try!"
My kid started copying it, so we steered her into using it for problem solving.
Elenor Wonders Why on PBS Kids. Each episode is ~ 20 minutes, broken into two ~ 10 minute stories. Cute animal kids explore nature and/or experiment in an inquiry-based manner. Many episodes have a song covering a history of science topic at the end of a segment. Animated with a calm, quiet aesthetic.
Adding on to my original answer, there are a bunch of shows on PBS Kids that will meet your criteria. Here are a few off the top of my head:
Cat in the Hat Knows a Lot About That. Covers nature and science topics. More about learning and interacting than experimenting. Also available on Tubi.
Work it Out Wombats. This one didn't appeal to my kids so I've seen just a couple of episodes, but it's about solving problems in a systematic manner.
Mega Wow. Live action. Only like 10 episodes but my kids are crazy about it right now. Hands on exploring of scientific topics.
Ada Twist, Scientist! It's about a little girl who is curious and with her two friends forms a hypothesis to test. Typically, each episode teaches some kind of physics or chemistry concept. My now four year old daughter has loved it for a year - so absolutely suitable for a 3.5 year old. Please follow up later to tell us what you found because I'm also interested in the answer to this beyond the typical PBS shows we watch.
PBS Kids has a show called Mega Wow that is well done. Scientific method with hypothesis and experiments, it was obviously made during pandemic so features a lot of kids via zoom.
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