401(k) contribution limits are not “per plan” but “per calendar year”. The amount you contributed into another plan in the current year will reduce the amount you can contribute to your new 401(k) plan.
When participating in two 401(k) plans in the same calendar year, neither your former employer nor your current employer must monitor how much you contribute in total for the year: it’s your responsibility to track this.  If you contribute too much, there are potential adverse tax implications to you when you file your tax return for that year.