[animation] Use register_apply_action for next_frame, prev_frame and set_frame (#19633)

tests/components/animation/common-actions.yaml

@@ -0,0 +1,9 @@
+button:
+  - platform: template
+    name: Animation Actions
+    on_press:
+      - animation.next_frame: rgb_animation
+      - animation.prev_frame: rgb_animation
+      - animation.set_frame:
+          id: rgb_animation
+          frame: 2

tests/components/animation/test-actions.esp8266-ard.yaml

@@ -0,0 +1,14 @@
+packages:
+  spi: !include ../../test_build_components/common/spi/esp8266-ard.yaml
+  animation: !include common.yaml
+  actions: !include common-actions.yaml
+
+display:
+  - platform: ili9xxx
+    id: animation_main_lcd
+    spi_id: spi_bus
+    model: ili9342
+    cs_pin: 5
+    dc_pin: 15
+    reset_pin: 16
+    invert_colors: false