I used to have a pair of nice light Lycra Specialized tights that were brilliant for slightly cool weather, but somehow I lost them. What else is available? Everything seems to be going on about how warm it is, but I don't want really warm I just want something to take the sting out of the cold air.
What's out there?
Knee warmers and decent warm socks with your normal bibs is a far better option, something like Castelli Nano or similar. I have a set of Kalf ones form Evans (don't even know if they still do them) and they're fantastic for exactly what you describe.
They keep your knees warm, which is vitally important once the air temperature starts to approach single figures, easily stuffed into your back pocket if it warms up.
Ha. I'm in the same boat - got some padless Specialized tights that are ideal for most cold conditions I'm likely to ride in (probably the same ones as you have), but they are getting increasingly worn - I think I've had them since 2008.
I've looked repeatedly for a replacement, but never really found anything, apart from running tights.
Just had a quick look and found these that look quite similar.
https://7mesh.com/seymour-tights
https://road.cc/content/review/269569-7mesh-seymour-tights
There's also these Lusso tights which you can have with the option of a pad or not, which is quite unusual.
https://www.lusso.bike/products/max-repel-tights?variant=28049741676646
Its a bit of a niche market. Its the kind of weather where I'd just wear 3/4 lengths or shorts and knee warmers.
There are loads of mid-weight tights out there that aren't especially warm - but I would still want it to be single digits before I put them on. Castelli tutto nano for example - nice mid-weight, and quite water-resistant.
I don't want leg warmers, they always seem to slip and be annoying generally. I like having my shins covered though as it makes spray more comfortable to endure.
I recently rediscovered knee warmers after 10 years or so. I used to hate them as they always slipped, but I dug them out in Feb and realised that if you pull them all the way up to just below your crutch they stay up. It was a revelation - I'd always just tucked them an inch or two inside my bibs and expected them to stay up.
Only problem now is that all my bib shorts are summer ones so I get pretty bad wind chill on my nether regions. Can't decide whether to try to find warm bib shorts with windproofing, or just get some 3/4 length bibs.
3/4 bibs that aren't too warm - these Gore ones look OK:
https://www.gorewear.com/uk/en-uk/c3-3-4-bib-tights-100569.html
Full length:
https://www.gorewear.com/uk/en-uk/c3-gore-windstopper-bib-tights-100337.html
Or stolen goat:
https://stolengoat.com/product/stolen-goat-orkaan-34-length-tights/
Full length:
https://stolengoat.com/product/stolen-goat-orkaan-full-length-weatherproof-bib-tights-mens/
(I've not tried any of the above!)
I bought a set of the Gore 3/4 and Thermo tights (not the windstoppers) linked last winter and got on well with them.  The 3/4 were not roubaix lined iirc so good for autumn / spring. I don’t often ride in extreme conditions though.
Just look for some running tights