I personally would go to Safelite. But you need to make sure they use the correct after-market windshield (there are three different OEM ones depending on your Trim level) and make sure you know who will re-calibrate the electronics that are associated with the windshield (if that is needed), as this usually must be done by the dealer, depending on what Trim Level you have.
One reason I would go with Safelite and their after-market windshield (if they in fact use an after market one), is that the OEM windshield seems to have an above-average failure rate (based on numerous complaints on this and other forums), and Safelite "may" have a better one. Even if Safelite uses the OEM windshield, they obviously have more experience in installing windshields (but I suspect many dealers farm that out anyway).
Here is one website among many that talk about this problem:
Two plaintiffs have filed a lawsuit against Hyundai in regards to windshields prematurely cracking on their 2020 Hyundai Palisades.
www.torquenews.com
For 2020 Palisades, here are the part numbers for the OEM windshields depending on Trim level and features required for each:
Part Number: 86111-S8090
Description: without head up display, without auto defog.
Part Number: 86111-S8100
Description: without head up display, with auto defog.
Part Number: 86111-S8110
Description: with head up display, with auto-defog