How does this compare to commercial tools? I read through the original Titan-2 paper and they were 5X faster in routing but achieved worse QoR compared to Quartus - does this close the gap?

I'm also wondering how congested these input designs are - I don't know much about the benchmarks used. Extremely congested designs can take a much, much longer time to route so an improvement there either in runtime or QoR could be useful.

Interesting, on a number of levels. Where exactly does VTR[1] fit into the current Open Source FPGA flow landscape?

[1] https://verilogtorouting.org/

Basically not. VTR is a research platform not really a tool used for real implementation. nextpnr is the tool for that. In that sense integration in VTR is nice but a few years back I would have hoped nextpnr would have become the standard. Much easier to compare fully open designs.