HDMI 2.1 would need to run of the same PCIe lane as TB4 so I would assume it can manage it.
PCIe has nothing to do with display output.
In an Intel Mac with discrete Thunderbolt controllers, the Thunderbolt controller has two separate DisplayPort 1.4 inputs.
It is similar for Macs with integrated Thunderbolt, such as the Intel Ice Lake MacBook Pro, or the Apple Silicon Macs.
HDMI 2.0 has max data rate of 14.4 Gbps.
30 bpp: 480 Mhz
24 bpp: 600 MHz (4K60 is 594 MHz)
20 bpp: 720 MHz (4:2:2 10 bpc)
18 bpp: 800 MHz (4:2:0 12 bpc)
16 bpp: 900 MHz (4:2:2 8 bpc)
15 bpp: 960 MHz (4:2:0 10 bpc)
12 bpp: 1200 MHz (4:2:0 8 bpc)
Apple usually uses DisplayPort HBR2 link rate, 12 bpp DSC, 12 bpc for the XDR (17.28 Gbps with 3:1 compression ratio so it's like 51.84 Gbps allowing a pixel clock of 1440 MHz).
30 bpp: 576 MHz (4K60 is 533MHz with HDR)
24 bpp: 720 MHz (4K80)
12 bpp: 1440 MHz (DSC for XDR display 1286 MHz)
8 bpp: 2160 MHz
DisplayPort 1.4 max link rate is HBR3 which is 25.92 Gbps.
30 bpp: 864 MHz (for HDR 4K95 is ≈858 MHz)
24 bpp: 1080 MHz (4K120 is ≈1075 MHz)
12 bpp: 2160 MHz (DSC)
8 bpp: 3240 MHz (DSC)
HDMI 2.1 max data rate is 42.67 Gbps (12 Gbps per lane but some displays may be limited to 10 Gbps per lane)
30 bpp: 1422 MHz (for HDR)
24 bpp: 1778 MHz
12 bpp: 3556 MHz (DSC)
8 bpp: 5333 MHz (DSC)
Notes:
- Gbps is data, not bits on the wire; we are ignoring 8b/10b encoding (or 16b/18b in the case of HDMI 2.1)
- DisplayPort 1.2 can support 4:2:2 while DisplayPort 1.4 and HDMI 2.1 can also support 4:2:0 but I skipped those since DSC is superior but I think DSC can work with 4:2:2 and 4:2:0 to allow even more pixels.
- Subtract 3% for FEC when DSC is being used.
HDMI 2.1 definitely can do more than DisplayPort 1.4, but DisplayPort 1.4 can do a lot more than HDMI 2.0 so it is useful to convert DisplayPort 1.4 to HDMI 2.1. If Apple allows DSC, then you should be able to get 4K240 or 8K60.
4K30 = 257 - 297 MHz
4K60 = 522 - 594 MHz
4K120, 8K30 = 1019 - 1188 MHz
4K240, 8K60 = 2068 - 2376 MHz
8K120 = 4258 - 4752 MHz (not possible with DisplayPort 1.4 except if you combine DSC with either 4:2:2 for 8bpc or 4:2:0 for 10bpc)