X509_get_signature_nid(), ASN1_STRING_get0_data(), RSA_bits() and DH_bits()
have been available since LibreSSL 2.7.
DSA_bits(), RSA_get0_n(), RSA_get0_e() will be available in LibreSSL 3.5.

Index: content/fetchers/about.c
--- a/content/fetchers/about.c
+++ b/content/fetchers/about.c
@@ -538,7 +538,8 @@ static nserror free_ns_cert_info(struct ns_cert_info *
 /* OpenSSL 1.0.x, 1.0.2, 1.1.0 and 1.1.1 API all changed
  * LibreSSL declares its OpenSSL version as 2.1 but only supports 1.0.x API
  */
-#if (defined(LIBRESSL_VERSION_NUMBER) || (OPENSSL_VERSION_NUMBER < 0x1010000fL))
+#if (defined(LIBRESSL_VERSION_NUMBER) && LIBRESSL_VERSION_NUMBER < 0x3050000fL) || \
+	(OPENSSL_VERSION_NUMBER < 0x1010000fL)
 /* 1.0.x */

 #if (defined(LIBRESSL_VERSION_NUMBER) || (OPENSSL_VERSION_NUMBER < 0x1000200fL))
@@ -609,7 +610,7 @@ static const BIGNUM *ns_RSA_get0_e(const RSA *r)
 #define ns_DH_bits DH_bits

 #else
-/* 1.1.1 and later */
+/* 1.1.1 and later, LibreSSL 3.5.0 and later */
 #define ns_X509_get_signature_nid X509_get_signature_nid
 #define ns_ASN1_STRING_get0_data ASN1_STRING_get0_data
 #define ns_RSA_get0_n RSA_get0_n

X509_up_ref has been available since LibreSSL 2.5.
X509_free has always been available.

Index: content/fetchers/curl.c
--- a/content/fetchers/curl.c
+++ b/content/fetchers/curl.c
@@ -92,7 +92,7 @@
 /* OpenSSL 1.0.x to 1.1.0 certificate reference counting changed
  * LibreSSL declares its OpenSSL version as 2.1 but only supports the old way
  */
-#if (defined(LIBRESSL_VERSION_NUMBER) || (OPENSSL_VERSION_NUMBER < 0x1010000fL))
+#if (OPENSSL_VERSION_NUMBER < 0x1010000fL)
 static int ns_X509_up_ref(X509 *cert)
 {
 	cert->references++;