Yes, you should get the excess amount (amount over 6.2%) refunded to you and ask for a new corrected W-2. Your employer is supposed to withhold 6.2% of your Social Security Wages (the Box 3 amount on your W-2), up to a maximum of $9,932.40 per taxpayer for tax year 2023. If one employer withheld too much Social Security tax, you won't be able to take a credit for the excess on your tax return. Also, see this Help Article - Excess Social Security Withheld
You can correct the Box 4 amount yourself before filing. Simply multiply the amount in Box 3 by a factor of 0.062 and enter that amount or 9,932.40 (whichever is less) in Box 4.
To get a refund for the excess withholding, fill out IRS Form 843: Claim for Refund and Request for Abatement according to the Form 843 Instructions and mail it in separately. Make a copy to keep with your tax return paperwork.
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