I found a clever solution to this. In the DI container, we usually register our dependencies during app initialization. However, it is fine to register a dependency in context. Here's a snippet of how I did it.

export function mountPrismaDatabase(app: OpenAPIHono<OpenAPIHonoConfig>) {
    app.use(async (c, next) => {
        // order is important here.
        // we initialize our prisma client connection first
        // and bind it to the context
        const adapter = new PrismaD1(c.env.DB);
        const client = new PrismaClient({ adapter });
        c.set('prisma', client);
        await next();
    });

    app.use(async (c, next) => {
        // we then register that context to our di container
        registerContextModule(applicationContainer, c);
        await next();
    });
}

I can then consume this dependency in my infrastructure.

type OAHonoContext = Context<OpenAPIHonoConfig>;

export class AuthenticationService implements IAuthenticationService {
    constructor(private _context: OAHonoContext) {}

    // ...code...

    createToken(session: Session): string {
        return jwt.sign(session.getData(), this._context.env.JWT_SECRET);
    }

    // ...code...
}

If you need more details, you may check this basic todo repo that I am currently using to practice clean architecture in my profile. I am linking the exact commit hash so that this link won't be broken when I move files around.