Two congruences involving harmonic numbers with applications

The harmonic numbers $H_n={\sum }_{0<k\le n}1\mathrm{/}k(n=0,1,2,\dots )$ play important roles in mathematics. Let $p>3$ be a prime. With helps of some combinatorial identities, we establish the following two new congruences: $$\sum _{k=1}^{p-1}\frac{\left(\genfrac{}{}{0px}{}{2k}{k}\right)}{k}{H}_k\equiv \frac{1}{3}\left(\frac{p}{3}\right)B_{p-2}\left(\frac{1}{3}\right)(\mathrm{m}\mathrm{o}\mathrm{d}p)$$ and $$\sum _{k=1}^{p-1}\frac{\left(\genfrac{}{}{0px}{}{2k}{k}\right)}{k}{H}_{2k}\equiv \frac{7}{12}\left(\frac{p}{3}\right)B_{p-2}\left(\frac{1}{3}\right)(\mathrm{m}\mathrm{o}\mathrm{d}p),$$ where $B_n(x)$ denotes the Bernoulli polynomial of degree $n$. As an application, we determine ${\sum }_{n=1}^{p-1}{g}_n$ and ${\sum }_{n=1}^{p-1}{h}_n$ modulo $p^3$, where $$g_n=\sum _{k=0}^n{\left(\genfrac{}{}{0px}{}{n}{k}\right)}^2\left(\genfrac{}{}{0px}{}{2k}{k}\right)\text{quadand}{h}_n=\sum _{k=0}^n{\left(\genfrac{}{}{0px}{}{n}{k}\right)}^2{C}_k$$ with $C_k=\left(\genfrac{}{}{0px}{}{2k}{k}\right)\mathrm{/}(k+1)$.