Go extension keeps prompting to update tools when switching between local and remote development environments with different goroots

(Issue opened after advice from @hyangah on Gophers Slack in this thread)

What version of Go, VS Code & VS Code Go extension are you using?

Run go version to get version of Go
- go version go1.15.5 linux/amd64
Run gopls -v version to get version of Gopls if you are using the language server.
- golang.org/x/tools/gopls v0.5.4
Run code -v or code-insiders -v to get version of VS Code or VS Code Insiders
- 1.51.1
Check your installed extensions to get the version of the VS Code Go extension
- v0.19.0

Run go env to get the go development environment details

GO111MODULE=""
GOARCH="amd64"
GOBIN=""
GOCACHE="/home/magi/.cache/go-build"
GOENV="/home/magi/.config/go/env"
GOEXE=""
GOFLAGS=""
GOHOSTARCH="amd64"
GOHOSTOS="linux"
GOINSECURE=""
GOMODCACHE="/home/magi/go/pkg/mod"
GONOPROXY=""
GONOSUMDB=""
GOOS="linux"
GOPATH="/home/magi/go"
GOPRIVATE=""
GOPROXY="https://proxy.golang.org,direct"
GOROOT="/usr/lib/go"
GOSUMDB="sum.golang.org"
GOTMPDIR=""
GOTOOLDIR="/usr/lib/go/pkg/tool/linux_amd64"
GCCGO="gccgo"
AR="ar"
CC="gcc"
CXX="g++"
CGO_ENABLED="1"
GOMOD=""
CGO_CFLAGS="-g -O2"
CGO_CPPFLAGS=""
CGO_CXXFLAGS="-g -O2"
CGO_FFLAGS="-g -O2"
CGO_LDFLAGS="-g -O2"
PKG_CONFIG="pkg-config"
GOGCCFLAGS="-fPIC -m64 -pthread -fmessage-length=0 -fdebug-prefix-map=/tmp/go-build550663058=/tmp/go-build -gno-record-gcc-switches"

Share the Go related settings you have added/edited

Run Preferences: Open Settings (JSON) command to open your settings.json file. Share all the settings with the go. or ["go"] or gopls prefixes.

{
    "go.useLanguageServer": true
}

Describe the bug

My main machine is running Archlinux with Go installed with pacman (so stuff installed in /usr/lib/go), but I often do development on a remote VM at work, which is running Fedora 33 with a manually-installed Go (so stuff is in /usr/local/go). Whenever I switch from local development to remote development (and vice versa) the Go extension pops up a message the current goroot is different than before, and then offers to update the Go tools.

From my point of view these two Go installations are completely unrelated so I don't see any benefit to continuously offer to update them solely based on the fact that they are located in different goroots.

Steps to reproduce the behavior:

Jump from local to remote SSH development on the same VS Code editor on a local and remote machine where the goroot of both Go installations is different.

golang / vscode-go