您可以尝试在data方法中显式键入this

import Vue from 'vue';

type Data = {
  a: number
}

export default Vue.extend({

  inject: ['b'],

  data(this: { b: string }): Data {
    const a = 3;
    const c = this.b
    return {
      a
    }
  },

  methods: {
    my_method() {
      this.a // no problem here
      this.b // ok
    }
  }
})

Playground
你可以看看Vue.extends类型定义：

export interface VueConstructor<V extends Vue = Vue> {
  new <Data = object, Methods = object, Computed = object, PropNames extends string = never>(options?: ThisTypedComponentOptionsWithArrayProps<V, Data, Methods, Computed, PropNames>): CombinedVueInstance<V, Data, Methods, Computed, Record<PropNames, any>>;
  // ideally, the return type should just contain Props, not Record<keyof Props, any>. But TS requires to have Base constructors with the same return type.
  new <Data = object, Methods = object, Computed = object, Props = object>(options?: ThisTypedComponentOptionsWithRecordProps<V, Data, Methods, Computed, Props>): CombinedVueInstance<V, Data, Methods, Computed, Record<keyof Props, any>>;
  new (options?: ComponentOptions<V>): CombinedVueInstance<V, object, object, object, Record<keyof object, any>>;

// we are interested in first
  extend<Data, Methods, Computed, PropNames extends string = never>(options?: ThisTypedComponentOptionsWithArrayProps<V, Data, Methods, Computed, PropNames>): ExtendedVue<V, Data, Methods, Computed, Record<PropNames, any>>;



 // ......
  extend<Data, Methods, Computed, Props>(options?: ThisTypedComponentOptionsWithRecordProps<V, Data, Methods, Computed, Props>): ExtendedVue<V, Data, Methods, Computed, Props>;
  extend<PropNames extends string = never>(definition: FunctionalComponentOptions<Record<PropNames, any>, PropNames[]>): ExtendedVue<V, {}, {}, {}, Record<PropNames, any>>;
  extend<Props>(definition: FunctionalComponentOptions<Props, RecordPropsDefinition<Props>>): ExtendedVue<V, {}, {}, {}, Props>;
  extend(options?: ComponentOptions<V>): ExtendedVue<V, {}, {}, {}, {}>;
}

因此，您可以提供显式泛型：

export default Vue.extend<Data, { my_method: () => void }, object, 'b'>({

  inject: ['b'],

  data(): Data {
    const a = 3;
    const c = this.b
    return {
      a
    }
  },

  methods: {
    my_method() {
      this.a // no problem here
      this.b // ok
    }
  }
})

使用vue-class-component和vue-property-decorator。
通过使用这些库，您可以编写像这样的强大的类型脚本代码。

@Component({
  layout: 'form',
  head: { title: 'somr title' },
  directives: { onlyNumber: onlyNumberDirective }
})
export default class Login extends Vue {
  @Ref()
  readonly form!: HTMLFormElement;
  
  phone = '';
  password = '';
  
  someMethod() {}

  get someComputedVar() {}
}

nuxt-property-decorator也合并上述库，使其更简单。

我也遇到了这种情况，这是我找到的解决方案：你应该像下面这样为nuxt写一个插件，并将其添加到插件部分的nuxt.config中。
所以对于第一个创建对象，Vue.extend

export const MyService = Vue.extend({

  data(){
    return {
      ready: false
    }
  },

  watch: {
    '$accessor.auth.loggedIn'(success){
        if (!success) return;

         this.ready = true;
        //do something here ...
     }
  },

  methods: {
    //...
  },

  
})

然后导出configure plugin函数如下：

export default function (ctx, inject) {

  const hookMixin = {
    created() {
      // nuxt context depends on $root object,
      // so here we assigning $root which just created

      const $root = this.$root;
      const myService = new MyService({
        beforeCreate() {
          this.$root = $root;
        }
      });

    //make $myService accessible globally
    Object.defineProperty(Vue.prototype, '$myService', {
      get() { return myService; }
    })

    },
  }

  // here adding global hook onMounted as mixin
  const mixins = ctx.app.mixins || [];
  mixins.push(hookMixin);
  ctx.app.mixins = mixins;
}

这里有三个步骤，你应该这样做，这个组件是全球可用的。
1.为nuxt注册created一个钩子，等待nuxt准备就绪。
1.当组件在beforeCreate准备就绪时，分配nuxt $root对象，您可以通过VueContructor options设置。
1.使服务全局化，以便通过Object. defineProperty通过$myService进行访问。
在这个例子中，我使用了存储变量loggedIn的watch。这里我也使用了typed-vuex，所以$accessor是一个全局访问器。逻辑很简单，我等待用户登录，然后我做一些事情。
享受您的定制组件！

是Nuxt3吗？
一定要换

import Vue from 'vue'
export default Vue.extend({...})

到

import { defineComponent } from 'vue';
export default defineComponent({ ... })