I’d imagine the basement stays relatively cool during the summers, as cold air sinks and being underground/partially underground the much smaller amount of sun it gets warms the walls less than those above ground. The heaters make sense because of water pipes and anything underground will be cooler when the ground is frozen.

No idea whether it is code where you are but your inspection person should be able to tell you - and note, even if it is allowed in principle, it still has to be done right. Probably not forbidden, but that's what the house inspection is for.

But: the general answer is pretty simple. The basement was finished later, and that's why it wasn't in the original HVAC system; most likely the owner who finished it looked into it and it would have been expensive or difficult.

You may want to get info and ask the inspector specifically about what kind of insulation was done in the basement when it was finished (and other aspects of how it was 'finished'). That might be more important than the baseboards. Both walls and floor of the basement.

Ground around the basement will tend to be warmer than outside air in winter, cooler in summer. That's normal - but you don't want to be heating the ground around the house (like an enormous heat sink) that much in winter, so that's why insulation is important. In summer, the concern is more about walls of the basement being cool when air is warmer and humid - can lead to condensation and mold.

This is a pretty complex topic and depends on local conditions, ask around and especially the inspector. They are issues that can be managed but obviously you don't want to find out later (or have to put much money in to fix).

In my area, I'd be far more concerned about the potential for moist damp conditions in summer than about electric baseboards - I have to run a dehumidifier in worst part of the summer, but it's manageable. My guess is baseboards could be improved/brought up to code more easily than dealing with a serious mold problem; and a slightly cold basement in winter is, well, just a bit cold.

What you have described is typical of a finished basement in the north. In summer the basement will be the coolest part of the house and there is no need for AC. Even when it is 90 outside this basement probably never goes above 75. The humidity level could be high so a dehumidifier may be needed.

In winter the basement will likely be in the mid 60s. It doesn't take many BTUs to raise the temperature since the walls are well insulated by the by the ground. The electric baseboard heaters will raise the temperature in a short time. You can turn them only when you are using the finished part of the basement.