Based on the 2024 CPS BMS codebook (page 4-6), the CPS defines the following terms:
Part-Time, Economic Reasons: The item includes slack work, material shortages, repairs to plant or equipment, start or termination of job during the week, and inability to find full-time work. (See also Full-Time Worker.)
Part-Time, Other Reasons (noneconomic reasons*): The item includes labor dispute, bad weather, own illness, vacation, demands of home housework, school, no desire for full-time work, and full-time worker only during peak season.
As for how to interpret these specific codes, the variable WKSTAT is a recode from the Census Bureau that states the part-time or full-time employment status for the respondent, and reasons. It is derived from a number of labor force questions asked in the monthly questionnaire. You should consider the response to WKSTAT as current as of the time of survey for that sample. So, for codes 12 and 21, they are current part-time workers, but typically work full-time. For code 15, they are currently working full-time hours, but typically work part-time hours. You may wish to use some of the other work-related variables to provide some context or verification for your analysis. It may be helpful to compare UHRSWORKT (usual hours worked per week at all jobs) and AHRSWORKT (actual hours worked, past week, at all jobs).
To your last question regarding “not at work”, you may want to use the variable ABSENT to cross-tabulate with WORKST. I see that for all those who reported “Not at work” for both full-time and part-time workers, ABSENT==3, meaning they were absent from work last week for “other reason (vacation, illness, labor dispute)”.