Retirement tax questions

Apologies for my ignorance. How do I know if I’m eligible to make a non-deductible contribution to a traditional IRA? My original concern was that the traditional IRA and 401k “buckets” are treated as one in the same, such that if I’m maxing out the 401k, I can’t pass any additional funds through the Traditional IRA (for purposes of funding the backdoor Roth) without exceeding the yearly max.