Are there any dedicated chips for measuring logic supply voltages?
Fundamentally, for your scenario, there will always be an ADC involved, yes. The analog value must get converted to a digital DN, and then from there passed to the host OS. The most common is analog voltage -> simple filter -> SAR ADC -> SMBus/I2C -> chipset/system management controller -> some kernel (or ACPI) driver -> host OS.

ADC topologies vary wildly, but a cheap and effective type is the SAR ADC, commonly found integrated into many MCUs. There's also sigma-delta and a few other types that are more geared towards specific applications and performance criteria. I imagine most converters used in your average SMBus/PMBus monitor-IC will probably 10 to 12 bits, with an internal voltage reference.

In terms of external components, it varies on the type of IC. The one I've linked below from LTC is built on a semiconductor process that can tolerate direct attachment of "high" voltages (>5.5V). I think at a bare minimum, you should have a RC filter on the input to act as an anti-aliasing filter for the ADC. That said, if you are sensing "high" voltages, you may want to consider isolation -- the LTC part I've linked below additionally has a variant supporting a split SDA output for exactly this reason, as it's not safe to have an IC that can sense/see voltages up to 80V galvanically/directly connected to the rest of your system.

Once you digitize it, it's a question about how to kick it further upstairs. For most PCs, it will be an SMBus-based approach. For the purposes of this answer, you can think of I2C and SMBus together -- simple, low-cost, two-wire busses that are open-drain in nature, ignoring the protocol differences. Modern chipsets (PCH for Intel) will have a SMBus controller that software can use to talk to monitoring chips / ICs to pull data over SMBus, or respond to alerts (i.e., a SMBus voltage monitor may trigger an alert in an under- or over-voltage condition).

Shopping-wise, you're basically looking for a SMBus or PMBus voltage/current monitor IC. For example, the LTC4151 would give you both current and voltage data for some load. Here is NXP's portfolio of such devices as well. Google 'SMBus/PMBus/I2C voltage monitor/ic' and you should see them show up -- TI, Maxim, Linear, NXP -- all the major guys are in this market.