An inferior solution to retaining current tab's context for new tabs

background.js

let windowContexts = {};
browser.windows.onRemoved.addListener(function(windowId) {
	delete windowContexts[windowId];
});
(async function() {
	try {
		let actives = await browser.tabs.query({
			active: true
		});
		if (actives?.length) {
			actives.forEach(tab => windowContexts[tab.windowId] = tab.cookieStoreId);
		}
	}
	catch (error) {
	}
})();
browser.tabs.onActivated.addListener(async function(activeInfo) {
	try {
		let tabInfo = await browser.tabs.get(activeInfo.tabId);
		windowContexts[activeInfo.windowId] = tabInfo.cookieStoreId;
	}
	catch (error) {
	}
});
browser.tabs.onCreated.addListener(function(tab) {
	if (
		tab.cookieStoreId === 'firefox-default'
		&& tab.url === 'about:newtab'
		&& windowContexts[tab.windowId]
		&& tab.cookieStoreId !== windowContexts[tab.windowId]
		&& !tab.incognito
		&& !tab.hidden
		&& tab.active
		&& tab.id !== browser.tabs.TAB_ID_NONE
	) {
		let tabRetained = {
			cookieStoreId: windowContexts[tab.windowId],
			active: tab.active,
			index: tab.index,
			windowId: tab.windowId,
			openerTabId: tab.openerTabId
		};
		browser.tabs.remove(tab.id);
		browser.tabs.create(tabRetained);
		return {
			cancel: true
		};
	}
});

manifest.json

{
	"browser_specific_settings": {
		"gecko": {
			"strict_min_version": "58.0a1"
		}
	},
	"background": {
		"scripts": [
			"background.js"
		]
	},
	"description": "Retain current container when creating new tabs.",
	"manifest_version": 2,
	"name": "Retainer",
	"permissions": [
		"tabs",
		"cookies"
	],
	"version": "0.1.0"
}

This is now a proper add-on: https://addons.mozilla.org/en-US/firefox/addon/retainer/

(@rickybrent)