Webpackerを使用しているRails6アプリにGemのtailwindcss-railsでTailwind CSSを導入し、YarnでdaisyUIを導入したところ、production環境でrake assets:precompile中にエラーが発生しました。
daisyUI以外のプラグインをYarnでインストールしても同じようなエラーが発生すると思います。

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remote:        Running: rake assets:precompile
remote:        node:internal/modules/cjs/loader:933
remote:          const err = new Error(message);
remote:                      ^
remote:
remote:        Error: Cannot find module 'daisyui'
remote:        Require stack:
remote:        - /tmp/build_3ec78e4d/config/tailwind.config.js
remote:        - /snapshot/tailwindcss/lib/cli.js
remote:        - /snapshot/tailwindcss/standalone-cli/standalone.js
remote:        1) If you want to compile the package/file into executable, please pay attention to compilation warnings and specify a literal in 'require' call. 2) If you don't want to compile the package/file into executable and want to 'require' it from filesystem (likely plugin), specify an absolute path in 'require' call using process.cwd() or process.execPath.
remote:            at Function.Module._resolveFilename (node:internal/modules/cjs/loader:933:15)
remote:            at Function._resolveFilename (pkg/prelude/bootstrap.js:1819:46)
remote:            at Function.Module._load (node:internal/modules/cjs/loader:778:27)
remote:            at Module.require (node:internal/modules/cjs/loader:1005:19)
remote:            at Module.require (pkg/prelude/bootstrap.js:1719:31)
remote:            at Module.require (/snapshot/tailwindcss/standalone-cli/standalone.js:21:22)
remote:            at require (node:internal/modules/cjs/helpers:94:18)
remote:            at Object.<anonymous> (/tmp/build_3ec78e4d/config/tailwind.config.js:8:13)
remote:            at Module._compile (node:internal/modules/cjs/loader:1101:14)
remote:            at Module._compile (pkg/prelude/bootstrap.js:1758:32) {
remote:          code: 'MODULE_NOT_FOUND',
remote:          requireStack: [
remote:            '/tmp/build_3ec78e4d/config/tailwind.config.js',
remote:            '/snapshot/tailwindcss/lib/cli.js',
remote:            '/snapshot/tailwindcss/standalone-cli/standalone.js'
remote:          ],
remote:          pkg: true
remote:        }
remote:        yarn install v1.22.17
remote:        [1/4] Resolving packages...
remote:        [2/4] Fetching packages...
remote:        [3/4] Linking dependencies...
remote:        warning " > daisyui@2.14.3" has unmet peer dependency "autoprefixer@^10.0.2".
remote:        warning " > daisyui@2.14.3" has unmet peer dependency "postcss@^8.1.6".
remote:        warning "daisyui > postcss-js@4.0.0" has unmet peer dependency "postcss@^8.3.3".
remote:        warning "daisyui > tailwindcss@3.0.24" has unmet peer dependency "postcss@^8.0.9".
remote:        [4/4] Building fresh packages...
remote:        Done in 13.21s.
remote:        Compiling...
remote:        Compiled all packs in /tmp/build_3ec78e4d/public/packs
remote:        Browserslist: caniuse-lite is outdated. Please run:
remote:          npx browserslist@latest --update-db
remote:          Why you should do it regularly: https://github.com/browserslist/browserslist#browsers-data-updating
remote:
remote:        Hash: a28352061b019b8d2a91
remote:        Version: webpack 4.46.0
remote:        Time: 3859ms
remote:        Built at: 05/17/2022 9:22:22 AM
remote:                                                Asset       Size  Chunks                         Chunk Names
remote:               js/application-6c08a5c51753ea590060.js   69.4 KiB       0  [emitted] [immutable]  application
remote:            js/application-6c08a5c51753ea590060.js.br   15.4 KiB          [emitted]
remote:            js/application-6c08a5c51753ea590060.js.gz   17.8 KiB          [emitted]
remote:           js/application-6c08a5c51753ea590060.js.map    205 KiB       0  [emitted] [dev]        application
remote:        js/application-6c08a5c51753ea590060.js.map.br   43.9 KiB          [emitted]
remote:        js/application-6c08a5c51753ea590060.js.map.gz   50.9 KiB          [emitted]
remote:                                        manifest.json  364 bytes          [emitted]
remote:                                     manifest.json.br  126 bytes          [emitted]
remote:                                     manifest.json.gz  142 bytes          [emitted]
remote:        Entrypoint application = js/application-6c08a5c51753ea590060.js js/application-6c08a5c51753ea590060.js.map
remote:        [0] (webpack)/buildin/module.js 552 bytes {0} [built]
remote:        [4] ./app/javascript/packs/application.js 480 bytes {0} [built]
remote:        [5] ./app/javascript/channels/index.js 205 bytes {0} [built]
remote:        [6] ./app/javascript/channels sync _channel\.js$ 160 bytes {0} [built]
remote:            + 3 hidden modules
remote:
remote:        Asset precompilation completed (22.28s)
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実行環境

Rails 6.1.4.1
Ruby 2.7.4
Webpcker 5.4.3
tailwindcss-rails 2.0.8

Gemのtailwindcss-railsでTailwind CSSを導入
yarn add daisyuiでdaisyUIを導入

config/tailwind.config.js

const defaultTheme = require('tailwindcss/defaultTheme');

module.exports = {
  content: ['./app/helpers/**/*.rb', './app/javascript/**/*.js', './app/views/**/*.{erb,haml,html,slim}'],
  theme: {
    extend: {},
  },
  plugins: [require('daisyui')],
};

Herokuにデプロイ
development環境ではエラーは発生していない

原因

rake assets:precompileでRakeタスクのyarn:installがtailwindcss:buildのあとに実行されるため

対処方法

yarn:installがtailwindcss:buildよりも前に実行されるようにする。

lib/tasks/tailwindcss.rake

Rake::Task['tailwindcss:build'].enhance(['yarn:install']) if Rails.env.production?

このコードが不要になったときに気づけるようにするなら

lib/tasks/tailwindcss.rake

def plugins?
  system('grep -q daisyui config/tailwind.config.js')
end

raise 'Consider removing this patch' unless Rails.version == '6.1.4.1' && Tailwindcss::VERSION == '2.0.8' && plugins?

Rake::Task['tailwindcss:build'].enhance(['yarn:install']) if Rails.env.production?

そもそも、Node.jsが必要なTailwind CSSのプラグインを使いたいならimportmap-railsやcssbundling-rails、jsbundling-railsなどを使ったほうがいいかも