How to check PCI type and version of free PCI slot in Linux shell

I know how to check how many PCI slots are not used yet on my server, by using dmidecode and looking for Available slots:

# dmidecode
[...]
Handle 0x0014, DMI type 9, 13 bytes
System Slot Information
    Designation: PCI1
    Type: 32-bit PCI
    Current Usage: Available
    Length: Long
    ID: 2
    Characteristics:
        5.0 V is provided
        PME signal is supported

and I also know how to check what PCI type and version are all the slots in the server (available and used), by using lspci -vvv and looking for LnkCap data:

# lspci -vvv
[...]
00:1f.0 PCI bridge: Silicon Integrated Systems [SiS] PCI-to-PCI bridge (prog-if 00 [Normal decode])
    [...]
    LnkCap: Port #0, Speed 2.5GT/s, Width x1, ...

where the speed of 2.5GT/s and the 1x suggest it's a PCI-e 1x slot. That's fine, but how do I relate these outputs to deduce what PCI type and version are the free slots in my server?

I initially tried to assume the Handle numbers of dmidecode matched the first column values in lspci output, but they don't. Any ideas?

EDIT

As per Mark Wagner's comment, the numbers between lspci and dmidecode do not match because lspci shows informations about a bridge, not a slot, and lspci doesn't show anything for unused slots. That means lspci is not useful in my case, my question is still the same, but likely the answer will not use lspci.