Bought a rose (Rosa) seedling online and it hasn't grown new roots after more than a month in the ground? It comes down to mainly these 2 reasons

The root system of a new rose seedling isn't developing; to use a more professional term, it isn't "settling into the pot." After the new seedling is planted, the roots don't extend out from the original root ball and take hold in the new soil. There are several reasons for this. The first is a difference in growing medium, the second is fertilizer and water management, and beyond that there are also details like care and season.
The first is a soil difference. For example, the root ball of the rose you bought is a prepared artificial growing medium with good aeration, while the medium you plant it in is loess, or what you bought is a seedling grown in yellow clay and what you plant it in is an artificial growing medium. This kind of structural difference between the original root ball medium and the later planting medium will restrict the development and extension of the root system. This is also why many gardening enthusiasts buy seedlings...
In the end the seedling dies, and when you dig it out you find that the roots never took hold in the new soil at all, meaning it never settled into the pot. So when planting a new seedling, never let the medium structure differ too much from that of the original root ball. The second is fertilizer and water management. Generally, after a seedling is planted, I sprinkle some controlled-release fertilizer on the surface of the potting soil, so that as the controlled-release fertilizer releases nutrients, it gradually induces the roots to grow into the new soil. This is the roots' tendency to grow toward fertilizer.
However, there are some other problems too, such as the seedling itself being very weak with insufficient growth, or not being acclimated well, causing the leaves' photosynthesis to be too weak to provide enough nutrients for root development, or the potting soil being too waterlogged, making it difficult for the roots to develop, or even adding too much base fertilizer, which burns the roots... Therefore, seedlings bought in spring generally settle into the pot quickly after planting because the climate is suitable and the seedling condition is good. This is also one seasonal reason.
So if you want a new seedling to settle in and grow at home as quickly as possible, you need to take good care of the roots. With sound roots comes a vigorous plant, along with proper pest and disease management and fertilizer and water management. Personally, when I grow roses, after receiving a seedling I generally don't pot it up right away. First I water it thoroughly, then spray a broad-spectrum fungicide (such as mancozeb), then place it in a shaded spot (ideally with dappled sunlight), and after about 3 days of acclimation I plant it. The results are quite good, and gardening enthusiasts can give it a try.