Unreasonably enormous memory usage with Kate on Windows since 3.8

Prerequisites

• Write a descriptive title.
• Make sure you are able to repro it on the latest version
• Search the existing issues.

Steps to reproduce

I don't know what exactly triggers this and narrowing it down isn't easy, but here's some possible steps:

1. Install Kate 23.08 on x64 Windows, using traditional installation.
2. Unpack PowerShellEditorServices somewhere convenient.
3. Create a PowerShell script like this:

mkdir -ErrorAction SilentlyContinue $env:TEMP/pses-qdls
& 'C:/PATH/TO/PSES/PowerShellEditorServices/Start-EditorServices.ps1' -BundledModulesPath C:/PATH/TO/PSES -LogPath $env:TEMP/pses-qdls/logs.log -SessionDetailsPath $env:TEMP/pses-qdls/session.json -FeatureFlags @() -AdditionalModules @() -HostName 'qdls' -HostProfileId 'qdls' -HostVersion 0.0.0 -Stdio -LogLevel Normal

4. Enable Kate's LSP client: Toggle on Settings > Configure Kate > Plugins > LSP Client, then apply.
5. Go to the Settings > Configure Kate > LSP Client > User Server Settings and add a block like this:

{
     "servers": {
          "powershell": {
              "command": ["pwsh", "-NoLogo", "-NoProfile", "-Command", "$PSStyle.OutputRendering = 'PlainText'; & C:/PATH/TO/PowerShellLanguageServer.ps1"],
              "highlightingModeRegex": "^PowerShell$"
          }
     }
}

6. Open Task Manager and watch the memory usage of the pwsh process Kate spawns as you browse around a large PowerShell project. Make sure you have a build of the project on $PSModulePath so PSES sees its functions etc.

Expected behavior

Reasonable memory usage.

Actual behavior

Memory usage of multiple Gbytes after running for a few minutes.

Error details

No response

Environment data

PS$> $PSVersionTable

Name                           Value
----                           -----
PSVersion                      7.3.6
PSEdition                      Core
GitCommitId                    7.3.6
OS                             Microsoft Windows 10.0.19043
Platform                       Win32NT
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0…}
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1
WSManStackVersion              3.0

Version

3.10.0, 3.9.0, 3.8.7; 3.7.3 not affected

Visuals

No response

Reproduce the memory growth using Kate, PowerShellEditorServices, Start-EditorServices.ps1, and PowerShellLanguageServer.ps1 while browsing a large project. Compare version 3.7.3 with 3.8.7 and later, then trace the LSP-driven process behavior; done means identifying and correcting the regression so pwsh maintains reasonable memory usage.