You can contribute to a traditional IRA no matter what your income is, but whether or not you can deduct the contribution depends on your income, filing status, and job situation. See here.
https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-ira-contribution-li...
Whether or not you can contribute to a Roth IRA also depends on your job, filing status and income, info at the same link.
Importantly, your participation may be limited if you "participate" in a retirement plan at work. You won't be participating in the plan at your new job for 2024 (even though they have a plan, you are not a participant yet), but you don't say if you participated in a retirement plan at your prior job. Unfortunately, if you participated even for only part of the year, that places you under the "participation" limits for IRA contributions for the whole year.
You sound like a good candidate for a "backdoor Roth IRA." This is where you make a non-deductible contribution to a traditional IRA, then roll it over to a Roth IRA. Your non-deductible IRA contribution is not limited by income or filing status, and the rollover is not taxable since the contribution was after-tax in the first place. The catch is that for this to really work, you must rollover/convert all your balances in traditional IRA accounts. (And note, if you have more than one IRA account, the balances are added together for this purpose. You may have multiple accounts, but the IRS considers you to have only one "individual retirement arrangement.")
If your total of all deductible/pre-tax traditional IRA accounts is just $2K, then the tax bill from a Roth conversion won't be too bad, and then you can do the backdoor Roth IRA method each year. Also importantly, you can do the backdoor Roth up to the full amount even if you max out your 401k contributions, because the two types of plans are controlled by different sections of the tax law and have different limits--one does not limit the other.
