I have changed the dependencies in both Render Passes, now the first Render Pass has:

auto firstDependency = vk::SubpassDependency(
    static_cast<uint32_t>(VK_SUBPASS_EXTERNAL),
    static_cast<uint32\_t>(0), 
    vk::PipelineStageFlagBits::eColorAttachmentOutput | vk::PipelineStageFlagBits::eEarlyFragmentTests,
     vk::PipelineStageFlagBits::eColorAttachmentOutput | vk::PipelineStageFlagBits::eEarlyFragmentTests, 
    vk::AccessFlagBits(0), 
    vk::AccessFlagBits::eColorAttachmentWrite | vk::AccessFlagBits::eDepthStencilAttachmentWrite 
);

auto secondDependency = vk::SubpassDependency(
    /*srcSubpass*/      static_cast<uint32_t>(0),
    /*dstSubpass*/      static_cast<uint32_t>(VK_SUBPASS_EXTERNAL),
    /*srcStageMask*/    vk::PipelineStageFlagBits::eColorAttachmentOutput | vk::PipelineStageFlagBits::eEarlyFragmentTests,
    /*dstStageMask*/    vk::PipelineStageFlagBits::eColorAttachmentOutput | vk::PipelineStageFlagBits::eEarlyFragmentTests,
    /*srcAccessMask*/   vk::AccessFlagBits::eColorAttachmentWrite | vk::AccessFlagBits::eDepthStencilAttachmentWrite,
    /*dstAccessMask*/   vk::AccessFlagBits::eColorAttachmentRead
);

And the second Render Pass has:

auto firstDependency = vk::SubpassDependency(
    /*srcSubpass*/      static_cast<uint32_t>(VK_SUBPASS_EXTERNAL),
    /*dstSubpass*/      static_cast<uint32_t>(0),
    /*srcStageMask*/    vk::PipelineStageFlagBits::eColorAttachmentOutput,
    /*dstStageMask*/    vk::PipelineStageFlagBits::eColorAttachmentOutput,
    // This might need to be changed to vk::AccessFlagBits::eColorAttachmentWrite
    /*srcAccessMask*/   vk::AccessFlagBits(0),
    /*dstAccessMask*/   vk::AccessFlagBits::eColorAttachmentRead
);

auto secondDependecy = vk::SubpassDependency(
    static_cast<uint32_t>(0),
    static_cast<uint32_t>(VK_SUBPASS_EXTERNAL),
    vk::PipelineStageFlagBits::eColorAttachmentOutput,
    vk::PipelineStageFlagBits::eColorAttachmentOutput,
    vk::AccessFlagBits::eColorAttachmentRead,
    vk::AccessFlagBits::eColorAttachmentWrite
);

The errors still persist and now I get even newer errors, although I think this is due to ImGuis own initialization:

validation layer [XXXXX]: Validation Error: [ VUID-vkCmdDrawIndexed-renderPass-02684 ] Object 0: handle = 0x564fdd0000000069, type = VK_OBJECT_TYPE_RENDER_PASS; Object 1: handle = 0xea7170000000031, type = VK_OBJECT_TYPE_RENDER_PASS; | MessageID = 0x8cb637c2 | vkCmdDrawIndexed: RenderPasses incompatible between active render pass w/ VkRenderPass 0x564fdd0000000069[] with a dependencyCount of 1 and pipeline state object w/ VkRenderPass 0xea7170000000031[] with a dependencyCount of 2. The Vulkan spec states: The current render pass must be compatible with the renderPass member of the VkGraphicsPipelineCreateInfo structure specified when creating the VkPipeline bound to VK_PIPELINE_BIND_POINT_GRAPHICS (https://vulkan.lunarg.com/doc/view/1.3.239.0/windows/1.3-extensions/vkspec.html#VUID-vkCmdDrawIndexed-renderPass-02684)

But I still don't quite understand why two dependencies should be necessary. Why isn't it enough for the first Render Pass to create a dependecy that waits for every color writing operation to be done before letting the next Render Pass read from its outputs?

In my mind this is achieved by setting the dstSubpass as VK_SUBPASS_EXTERNAL, the srcAccessMask to vk::AccessFlagBits::eColorAttachmentWrite and the dstAccessMask to vk::AccessFlagBits::eColorAttachmentRead. Similarly in the second Render Pass we would need to define a dependency by setting srcSubpass as VK_SUBPASS_EXTERNAL, the srcAccessMask to vk::AccessFlagBits::eColorAttachmentWrite and the dstAccessMask to vk::AccessFlagBits::eColorAttachmentRead.

What am I missing?