I came across this just recently as well. I could not find an appropriate typings package from DefinitelyTyped so I started extrapolating from my own usage and the Metamask Documentation and created something that works so far.
Perhaps the community could edit this answer with their own contributions.
In order to use the ethereum object without TS complaints, I declare it in the window object:
declare global {
    interface Window {
        ethereum: Ethereumish;
    }
}
The makeshift Ethereum Provider types, Ethereumish looks like this:
import { ProviderMessage, ProviderRpcError, ProviderConnectInfo, RequestArguments } from 'hardhat/types';
export interface EthereumEvent {
    connect: ProviderConnectInfo;
    disconnect: ProviderRpcError;
    accountsChanged: Array<string>;
    chainChanged: string;
    message: ProviderMessage
}
type EventKeys = keyof EthereumEvent;
type EventHandler<K extends EventKeys> = (event: EthereumEvent[K]) => void;
export interface Ethereumish {
    autoRefreshOnNetworkChange: boolean;
    chainId: string;
    isMetaMask?: boolean;
    isStatus?: boolean;
    networkVersion: string;
    selectedAddress: any;
    on<K extends EventKeys>(event: K, eventHandler: EventHandler<K>): void;
    enable(): Promise<any>;
    request?: (request: { method: string, params?: Array<any> }) => Promise<any>
    /**
     * @deprecated
     */
    send?: (request: { method: string, params?: Array<any> }, callback: (error: any, response: any) => void) => void
    sendAsync: (request: RequestArguments) => Promise<unknown>
}
As you can see, I have not been able to figure out the exact types of many things so far, but the important methods, send and sendAsync are accurate in my experience.
Another useful template is something I found inside @ethersproject/providers/src.ts/web3-provider.ts
export type ExternalProvider = {
    isMetaMask?: boolean;
    isStatus?: boolean;
    host?: string;
    path?: string;
    sendAsync?: (request: { method: string, params?: Array<any> }, callback: (error: any, response: any) => void) => void
    send?: (request: { method: string, params?: Array<any> }, callback: (error: any, response: any) => void) => void
    request?: (request: { method: string, params?: Array<any> }) => Promise<any>
}
this can be used when loading a new provider
new ethers.providers.Web3Provider(myProvider: ExternalProvider)