Can I use
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Session history management

- LS

Method of manipulating the user's browser's session history in JavaScript using history.pushState, history.replaceState and the popstate event.

Chrome

  1. 4: Not supported
  2. 5 - 109: Supported
  3. 110: Supported
  4. 111 - 113: Supported

Edge

  1. 12 - 108: Supported
  2. 109: Supported

Safari

  1. 3.1 - 4: Not supported
  2. 5 - 5.1: Partial support
  3. 6 - 16.2: Supported
  4. 16.3: Supported
  5. TP: Supported

Firefox

  1. 2 - 3.6: Not supported
  2. 4 - 108: Supported
  3. 109: Supported
  4. 110 - 111: Supported

Opera

  1. 9 - 11.1: Not supported
  2. 11.5 - 93: Supported
  3. 94: Supported

IE

  1. 5.5 - 9: Not supported
  2. 10: Supported
  3. 11: Supported

Chrome for Android

  1. 109: Supported

Safari on iOS

  1. 3.2 - 4.1: Not supported
  2. 4.2: Partial support
  3. 5 - 16.2: Supported
  4. 16.3: Supported

Samsung Internet

  1. 4 - 18.0: Supported
  2. 19.0: Supported

Opera Mini

  1. all: Not supported

Opera Mobile

  1. 10 - 11: Not supported
  2. 11.1 - 12.1: Supported
  3. 73: Supported

UC Browser for Android

  1. 13.4: Supported

Android Browser

  1. 2.1: Not supported
  2. 2.2 - 2.3: Supported
  3. 3 - 4.1: Not supported
  4. 4.2 - 4.4.4: Supported
  5. 109: Supported

Firefox for Android

  1. 109: Supported

QQ Browser

  1. 13.1: Supported

Baidu Browser

  1. 13.18: Supported

KaiOS Browser

  1. 2.5: Supported

Older iOS versions and Android 4.0.4 claim support, but implementation is too buggy to be useful.

Resources:
MDN Web Docs - Manipulating the browser history
History.js polyfill
Demo page
has.js test
WebPlatform Docs
Introduction to history management