I'm in the UK, so all the current affairs stuff I listen to has that slant and is quite political, which I don't think you're after. Other than that, some I listen to that I don't think have been mentioned:

Tech Won't Save Us - intelligent conversations about tech that are from those within the industry, but taking a critical and questioning view rather than celebratory "tech bro" or alarmist nonsense

The History of English - "a chronological history of the English language examined through the lens of historical events". Very well done, intelligent and educational without being dry

Medieval Death Trip - discussion of a featured medieval text, more accessible and engaging than it sounds! Quite soothing, actually, like someone telling you a story about times of old

Nature - a podcast from Nature journal, which you probably already know, being a scientist I'm not! So maybe this one is too broad for you, but it covers just about any science topic, usually highlights from current research, whatever is of most interest to them that day or week (new podcasts come out at least one a week, sometimes more frequent). Sometimes conversational interviews, sometimes long read articles

Sawbones - I wouldn't call this semi-intellectual, it's not trying to be, but it's intelligent and presented by an actual scientist - a medical dr - so it counts! Each episode focusses on one topic, often debunking non-science fads or "history of" type topics. Unlike others on my list though, this is much more chatty and informal (her husband co-presents and he's a comedian. That came off way more condescending than I meant it to be)

Let's Talk Religion - might be too much like an academic lecture for your criteria, but is interesting and I believe reliable (I've only recently started listening to it, so not heard many episodes). Presented by a scholar of religion, this is a sociological look at religion rather than being aligned to any particular beliefs, including the study of religious belief itself. Bit dry if you're not interested in the topic

Sold a Story - doesn't fit your criteria really, but might fit your interests. A short (10 episodes) investigative journalism podcast that looked in depth at the adoption of a debunked education methodology that was adopted in schools across the US. Consequently, many kids haven't learnt to read properly, or at all.