The linux kernel patches for fu740 say it is a Synopsys Designware PCIe host controller. This is licensed IP so there are probably restrictions on what we can say about it. You might be able to get more info from Synopsys. Or by looking at various open source support for Synopsis Designware PCIe IP. The linux kernel patches for instance contain a lot of useful info.
https://github.com/sifive/meta-sifive/blob/2021.05/recipes-kernel/linux/files/0013-dt-bindings-PCI-Add-SiFive-FU740-PCIe-host-controlle.patch
https://github.com/sifive/meta-sifive/blob/2021.05/recipes-kernel/linux/files/0015-riscv-dts-Add-PCIe-support-for-the-SiFive-FU740-C000.patch
The ASMedia part is a PCIe switch. I’m not an expert in this area, but I would guess this works autonomously and you don’t have to worry about programming it. I don’t see linux kernel patches that mention ASMedia.