The Russian army has been continuously storming the Kharkov region from Volchansk since May 10. The invaders entered the border Volchansk in the first days, having previously destroyed the minefields with the help of artillery and corrective bombs. They entered, but never progressed further.
This is another lie, my little lying friend: Vovchansk is 10km away from the border. Between Vovchansk and the border there are many villages which had to be captured en route to Vovchansk, which also took some time. So, no, Russia hasn't been holding Vovchansk under siege since May 10. 
Sources:
https://lenta.ru/news/2024/05/13/volchansk/
https://www.rbc.ua/ukr/news/vovchansk-mapi-boyovih-diy-shcho-vidbuvaetsya-1715594128.html
https://uatv.ua/v-5-km-ot-granitsy-s-rossiej-pod-postoyannymi-obstrelami-i-bez-gaza-kak-vyzhivayut-okolo-4000-chelovek-ostayushhihsya-v-volchanske- video/
Since the entire border territory of the Kharkov region was under constant fire from Russian troops, there was practically no first line of defense there.
According to the statement of the commander of the Ukrainian reconnaissance company fighting in this direction, Denis Yaroslavsky, the first line of defense near Volchansk allegedly “simply did not exist” and the Russians “went on foot” to this town without any resistance.
The second or third line of defense was 10-15-20 and even 30 km away from the border or front line, however, they were also under fire from the invaders, who destroyed construction equipment and the civilian builders themselves. Therefore, more than 30 types of various civil construction equipment were destroyed.
https://www.bbc.com/russian/articles/c97z71jwe7wo
It is worth recognizing that despite the statements of the Ukrainian authorities, this territory was not prepared for defense, which explains the relatively quick takeover of this border theory by the Russians. However, after almost a month of Russian offensive, the occupiers cannot advance further than Volchansk. Moreover, a significant part of this town is still not only controlled by the Ukrainian Armed Forces, but also the occupiers are being pushed out of some of its neighborhoods. In general, the Russian offensive in the Kharkov region has been stopped, their idea has completely failed.
After the ban on the Ukrainian Armed Forces striking military targets on Russian territory with Western weapons was lifted, columns of Russian equipment are destroyed even before they cross the Ukrainian border.