You have asked a very incisive and important question. Nevertheless, the basic core of this question has been answered before, here. In sum, the determination is rather simple. As summarized from NOAA in that answer -
The 2020 global surface temperature was 1.76°F warmer than 57.0°F, which is 58.76°F. This temperature is 2.14°F warmer than the pre-industrial period (1880-1900). Consequently, the pre-industrial period temperature was 58.76°F - 2.14°F, or approximately 56.62°F (13.68°C).
The current average global temperature can be determined for any one year but is usually only an estimate based on the most recently assessed information. The raw data consists of substantially many hundreds of thousands of global sub-hourly/hourly/daily measurements from which the global average temperature is determined. These measurements are taken, recorded, and reported, for many thousands of measurement sites on land, ships at sea, and aerial measurements by aircraft and balloons. These data are adequately summarized for an average annual global surface temperature, and are available on the internet from the IPCC, British Met Office, NOAA, and others. Although there may be slight differences in the time series presented by any particular entity (NOAA, for instance), these time series for the historic global average temperature are quite consistent and comparable.
The pre-industrial temperature record is similarly assessed, based upon established meteorological sites and reported readings during the pre-1900 time period back to about 1850. Keep in mind that as time recedes before 1900, land-based measurement sites become increasingly few and reported measurements increasingly sparse. Hence, the average temperature for the pre-industrial period is established by statistical comparisons and adjustments for concurrent and comparable records later in the early 20th century. Although the time series for these individual records forms the basis for determining the pre-industrial average temperature, the key word is average. Consequently, as an average, the estimate is reasonably good because variations away from the average affect the outcome by a very small margin.
As you have asked -
What is the baseline temperature for the climate-change debate...
the answer is 13.68°C.