I recorded both lspci -vvvv and lspci -xxxx for the following connections:

  - hotplug: when GPU is connected after the host was loaded
  - fresh: when GPU is connected before the host was started

The main difference is the following:

1c1
< # hotplug
---
> # fresh
6c6
< 	Control: I/O+ Mem- BusMaster- SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-
---
> 	Control: I/O- Mem+ BusMaster- SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-
8c8
< 	Interrupt: pin A routed to IRQ 18
---
> 	Interrupt: pin A routed to IRQ 255
10,13c10,14
< 	Region 1: Memory at <unassigned> (64-bit, prefetchable) [disabled]
< 	Region 3: Memory at <unassigned> (64-bit, prefetchable) [disabled]
< 	Region 5: I/O ports at 4000 [size=128]
< 	Expansion ROM at f1400000 [virtual] [disabled] [size=512K]
---
> 	Region 0: Memory at f0000000 (32-bit, non-prefetchable) [size=16M]
> 	Region 1: Memory at c0000000 (64-bit, prefetchable) [size=256M]
> 	Region 3: Memory at d0000000 (64-bit, prefetchable) [size=32M]
> 	Region 5: I/O ports at 4000 [disabled] [size=128]
> 	Expansion ROM at f1080000 [disabled] [size=512K]
30c31
< 		LnkSta:	Speed 5GT/s (downgraded), Width x1 (downgraded)
---
> 		LnkSta:	Speed 2.5GT/s (downgraded), Width x1 (downgraded)
35a37
> 			 AtomicOpsCap: 32bit- 64bit- 128bitCAS-
79c81
< 	Interrupt: pin B routed to IRQ 19
---
> 	Interrupt: pin B routed to IRQ 255
81c83
< 	Region 0: Memory at f1480000 (32-bit, non-prefetchable) [size=16K]
---
> 	Region 0: Memory at f1000000 (32-bit, non-prefetchable) [size=16K]
98c100
< 		LnkSta:	Speed 5GT/s (downgraded), Width x1 (downgraded)
---
> 		LnkSta:	Speed 2.5GT/s (downgraded), Width x1 (downgraded)
124,125c126,127

I can tell, that hotplug connects as 5GT/s and fresh - 2.5GT/s. And there is an obvious difference between Regions.

The difference between lspci -xxxx but I don't know how to interpret the result:

124,125c126,127
< 00: de 10 03 1c 01 00 10 00 a1 00 00 03 00 00 80 00
< 10: 00 00 00 00 0c 00 00 00 00 00 00 00 0c 00 00 00
---
> 00: de 10 03 1c 02 00 10 00 a1 00 00 03 10 00 80 00
> 10: 00 00 00 f0 0c 00 00 c0 00 00 00 00 0c 00 00 d0
127c129
< 30: 00 00 00 00 60 00 00 00 00 00 00 00 00 01 00 00
---
> 30: 00 00 f8 ff 60 00 00 00 00 00 00 00 ff 01 00 00
132c134
< 80: 10 29 09 00 03 3d 45 00 43 01 12 10 00 00 00 00
---
> 80: 10 29 09 00 03 3d 45 00 43 01 11 10 00 00 00 00
198c200
< 4a0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 78
---
> 4a0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ff
221c223
< 610: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
---
> 610: 01 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00
257c259
< 850: 00 00 00 00 78 00 00 00 ff 3f 00 00 00 00 00 00
---
> 850: 00 00 00 00 af 04 00 00 ff 3f 00 00 00 00 00 00
382,383c384,385
< 00: de 10 f1 10 02 00 10 00 a1 00 03 04 00 00 80 00
< 10: 00 00 48 f1 00 00 00 00 00 00 00 00 00 00 00 00
---
> 00: de 10 f1 10 02 00 10 00 a1 00 03 04 10 00 80 00
> 10: 00 00 00 f1 00 00 00 00 00 00 00 00 00 00 00 00
385c387
< 30: 00 00 00 00 60 00 00 00 00 00 00 00 00 02 00 00
---
> 30: 00 00 00 00 60 00 00 00 00 00 00 00 ff 02 00 00
390c392
< 80: 10 29 09 00 03 3d 45 00 43 01 12 10 00 00 00 00
---
> 80: 10 29 09 00 03 3d 45 00 43 01 11 10 00 00 00 00
456,457c458,459
< 4a0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 78
< 4b0: 78 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
---
> 4a0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ff
> 4b0: af 04 00 00 00 00 00 00 00 00 00 00 00 00 00 00