It is approaching full employment, yes. You can see this by looking at U6[1] which includes anyone who has been seeking employment within the previous 12 months but have been unable to secure a job and has not searched for work in the past four weeks. It also includes anyone who has gone back to school, become disabled, and people who are underemployed or working part-time hours. It's down to where it was in early 2019. The Labor Force Participation Rate is not a measure of employment unless you think the employment rate was lower in 2019 than it was in 2008[2]. The pandemic prompted more older workers to retire but it's just continuing an existing trend in an aging country.
There is a canonical definition and that's just that there is no more demand-deficient unemployment. Meaning it doesn't even require U3 to hit 0 let alone LFPR to hit 100%. It allows for churn, underemployment as well as unemployables. It's not a metric of achieving utopia, just a situation with almost no slack in the labor market for employers.
[1]https://fred.stlouisfed.org/series/U6RATE
[2]https://www.bls.gov/charts/employment-situation/civilian-lab...