[rush] Make `install` and `update` log package manager to a file in common/temp

[dmichon-msft]

Summary

For diagnosing missing peer dependency issues, the log output of pnpm install is very useful, but by default rush update only writes to the console and the output can be so long that it isn't available in the back buffer.

It would be useful to always log to a file under common/temp so that when issues are encountered, one can look back at the log from the most recent install to find the offending packages.

Standard questions

Please answer these questions to help us investigate your issue more quickly:

Question	Answer
@microsoft/rush globally installed version?	5.118.7
rushVersion from rush.json?	5.118.7
useWorkspaces from rush.json?	true
Operating system?	Linux
Would you consider contributing a PR?	Yes
Node.js version (node -v)?	18.19.1