もしかすると

これで解決するかも？

https://qiita.com/siruku6/items/701ca518c126dc5ba571

tl; dr

npm install aws-cdk@2.18.0

何が起きるか

2.20.0 を入れようとすると

% npm install aws-cdk@2.20.0
npm WARN tar zlib: incorrect data check
npm WARN tarball cached data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.20.0.tgz (sha512-rs9LTpvrlbsMcenZ3t7TuLDGbHhbnDocrE63Xb2PT++VptR/A8svllK8k1W7hPl77L9QS75GNK5gh+ShkEzsnw==) seems to be corrupted. Refreshing cache.
npm WARN tarball tarball data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.20.0.tgz (sha512-rs9LTpvrlbsMcenZ3t7TuLDGbHhbnDocrE63Xb2PT++VptR/A8svllK8k1W7hPl77L9QS75GNK5gh+ShkEzsnw==) seems to be corrupted. Trying again.
npm WARN tar zlib: incorrect data check
npm WARN tarball tarball data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.20.0.tgz (sha512-rs9LTpvrlbsMcenZ3t7TuLDGbHhbnDocrE63Xb2PT++VptR/A8svllK8k1W7hPl77L9QS75GNK5gh+ShkEzsnw==) seems to be corrupted. Trying again.
npm ERR! code Z_DATA_ERROR
npm ERR! errno -3
npm ERR! zlib: incorrect data check

npm ERR! A complete log of this run can be found in:
npm ERR!     /Users/user/.npm/_logs/2022-04-14T12_39_20_908Z-debug-0.log

2.19.0 を入れようとすると

% npm install aws-cdk@2.19.0
npm WARN tar zlib: incorrect data check
npm WARN tarball cached data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.19.0.tgz (sha512-qOwxDKd1xKsiBW3laYrFBiAF510okJvslEeHViO08SKIyhitUe/HTn2iqfdVBb/zF6wSdm/sRsj2WNHpiKFcBQ==) seems to be corrupted. Refreshing cache.
npm WARN tarball tarball data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.19.0.tgz (sha512-qOwxDKd1xKsiBW3laYrFBiAF510okJvslEeHViO08SKIyhitUe/HTn2iqfdVBb/zF6wSdm/sRsj2WNHpiKFcBQ==) seems to be corrupted. Trying again.
npm WARN tar zlib: incorrect data check
npm WARN tarball tarball data for aws-cdk@https://registry.npmjs.org/aws-cdk/-/aws-cdk-2.19.0.tgz (sha512-qOwxDKd1xKsiBW3laYrFBiAF510okJvslEeHViO08SKIyhitUe/HTn2iqfdVBb/zF6wSdm/sRsj2WNHpiKFcBQ==) seems to be corrupted. Trying again.
npm ERR! code Z_DATA_ERROR
npm ERR! errno -3
npm ERR! zlib: incorrect data check

npm ERR! A complete log of this run can be found in:
npm ERR!     /Users/user/.npm/_logs/2022-04-14T12_39_31_004Z-debug-0.log

こんな感じです。

何度 trying againg しても改善されず、配信経路のどこかがぶっ壊れてると思うので、今は大人しく v1 系とか v2.18.0 を使うのが安定っぽいです。

NOTICES

19836 AWS CDK v1 entering maintenance mode soon

    Overview: AWS CDK v1 is entering maintenance mode on June 1, 2022.
              Migrate to AWS CDK v2 to continue to get the latest features
              and fixes!

    Affected versions: framework: 1.*, cli: 1.*

    More information at: https://github.com/aws/aws-cdk/issues/19836

(こんな感じでv2にしろと焦らせてきますが、今やるのは多分まずい気がします。まともに動くものが出ていない。)